{"id":248,"date":"2023-07-10T13:40:44","date_gmt":"2023-07-10T13:40:44","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%81%d0%b8%d0%bc%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%87%d0%bd%d0%b0%d1%8f-%d1%82%d0%be%d1%87%d0%ba%d0%b0-%d1%83%d1%87%d0%b8%d1%82%d1%8b%d0%b2%d0%b0%d1%8f-%d0%b4%d1%80%d1%83%d0%b3%d1%83%d1%8e-%d1%82\/"},"modified":"2023-07-10T13:40:44","modified_gmt":"2023-07-10T13:40:44","slug":"%d1%81%d0%b8%d0%bc%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%87%d0%bd%d0%b0%d1%8f-%d1%82%d0%be%d1%87%d0%ba%d0%b0-%d1%83%d1%87%d0%b8%d1%82%d1%8b%d0%b2%d0%b0%d1%8f-%d0%b4%d1%80%d1%83%d0%b3%d1%83%d1%8e-%d1%82","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%81%d0%b8%d0%bc%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%87%d0%bd%d0%b0%d1%8f-%d1%82%d0%be%d1%87%d0%ba%d0%b0-%d1%83%d1%87%d0%b8%d1%82%d1%8b%d0%b2%d0%b0%d1%8f-%d0%b4%d1%80%d1%83%d0%b3%d1%83%d1%8e-%d1%82\/","title":{"rendered":"\u0422\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"punto-simetrico-respecto-a-otro-punto\"><\/span> \u0422\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0435<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043c\u044b \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438:<\/p>\n<p> <strong>\u0422\u043e\u0447\u043a\u0430 \u0410&#8217; \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u041c, \u0435\u0441\u043b\u0438 \u0442\u043e\u0447\u043a\u0430 \u0410&#8217; \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0430 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e \u043d\u0430 \u0442\u043e\u043c \u0436\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0438 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \u041c, \u0447\u0442\u043e \u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u0410 \u0438 \u041c. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u041c \u2013 \u044d\u0442\u043e \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0430, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u043e\u0433\u043e \u0442\u043e\u0447\u043a\u0438 \u0410 \u0438 \u0410&#8217;.<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/point-symetrique-par-respect-dun-autre-point.webp\" alt=\"\u0442\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0435\" class=\"wp-image-2568\" width=\"224\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b245228198e894b500e680fba0da85a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,M) = d(A',M )\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043c\u044b \u0442\u0430\u043a\u0436\u0435 \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u0442\u043e\u0447\u043a\u0430 \u041c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0446\u0435\u043d\u0442\u0440\u043e\u043c \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438.<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f  \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u044b \u043e\u0442\u0440\u0435\u0437\u043a\u0430  :<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89899129b0d44c4cd976ad3e49613dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{A+A'}{2}=M\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"95\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438\u0437\u0432\u043b\u0435\u043a\u0430\u0435\u043c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u0410&#8217; \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c <strong>\u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u0442\u043e\u0447\u043a\u0438, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438:<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7f086fbd1244c016821d618224d85d1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{orange} \\boxed{ \\color{black} \\quad A' = 2M - A \\quad \\vphantom{\\Bigl)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"246\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-el-punto-simetrico-respecto-a-otro-punto\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u043a\u0438, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0442\u043e\u0447\u043a\u0443 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u0442\u043e\u0447\u043a\u0438 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 \u041c. \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da59d3cf0aad36a3cc97ba45f400fcf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,3,0) \\qquad \\qquad M(-1,4,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043c\u0435\u0436\u0434\u0443 \u044d\u0442\u0438\u043c\u0438 \u0434\u0432\u0443\u043c\u044f \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd271153fefe3118d9443db8d7e2bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A' = 2M - A\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u0442\u043e\u0447\u043a\u0438 \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa87525f5b34bdcef7b82eb336078a8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A' = 2(-1,4,2) -(1,3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0418 \u043c\u044b \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u043c: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0c48dd83cd17af141e618108f5a84ce0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A' = (-2,8,4) -(1,3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"188\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-409d4dd835ed4cfa11e51b615bf6d6df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{A'=(-3,5,4)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"punto-simetrico-respecto-a-una-recta\"><\/span> \u0442\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u043f\u0440\u044f\u043c\u043e\u0439 \u043b\u0438\u043d\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0442\u043e\u0447\u043a\u0438, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438. \u041d\u0443, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0441\u0442\u044c \u0442\u043e\u0447\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043b\u0438\u043d\u0438\u0438 \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u0445\u043e\u0436\u0430:<\/p>\n<p> <strong>\u0422\u043e\u0447\u043a\u0430 \u0410&#8217; \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439, \u0435\u0441\u043b\u0438 \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438 \u0410&#8217; \u0438 \u0410 \u043b\u0435\u0436\u0430\u0442 \u043d\u0430 \u043e\u0434\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439, \u0438 \u043f\u0440\u0438 \u044d\u0442\u043e\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u043e\u0439 \u0410&#8217; \u0438 \u043f\u0440\u044f\u043c\u043e\u0439 \u0440\u0430\u0432\u043d\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u043e\u0439 \u0410 \u0438 \u043b\u0438\u043d\u0438\u0435\u0439.<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/point-symetrique-par-rapport-a-une-droite.webp\" alt=\"\u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0442\u043e\u0447\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439\" class=\"wp-image-2586\" width=\"470\" height=\"362\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82482dab7ac516792922108f81d4b657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,r)= d(A',r)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043b\u0438\u043d\u0438\u044f <em>r<\/em> \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0441\u044c\u044e \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u0430\u043c\u0438.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u0442\u043e\u0447\u043a\u0438 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439 <em>r<\/em> \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0443:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u041d\u0430\u0445\u043e\u0434\u0438\u043c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0443\u044e \u043f\u0440\u044f\u043c\u043e\u0439 <em>r<\/em> , \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \u0410 (\u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u03c0 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0433\u043e \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f). \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u0443\u0434\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043a \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">\u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c  \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f  \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0440\u044f\u043c\u043e\u0439 (\u0442\u043e\u0447\u043a\u0430 \u041c \u043d\u0430 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0438).<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">\u041c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0441\u0442\u0438 \u0442\u043e\u0447\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 (\u0441\u043c. \u0440\u0430\u0437\u0434\u0435\u043b \u0432\u044b\u0448\u0435), \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u0442\u043e\u0447\u043a\u0438 A \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 M. \u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0438\u0441\u043a\u0430\u043b\u0438.<\/span> <\/li>\n<\/ol>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-el-punto-simetrico-respecto-a-una-recta\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0443\u0437\u043d\u0430\u0435\u043c, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0440\u0435\u0448\u0435\u043d\u043d\u043e\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435:<\/p>\n<ul>\n<li> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0442\u043e\u0447\u043a\u0443, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0435 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439 r. \u041a\u0430\u043a \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u0441\u044f, \u0442\u043e\u0447\u043a\u0430 \u0438 \u043b\u0438\u043d\u0438\u044f:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e5906f8f5fce95109f9f19d93d1f41cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A(4,0,-1) \\qquad \\qquad r: \\ \\begin{cases}x=1 + t \\\\[1.7ex] y=5 +4t\\\\[1.7ex] z=-4-3t \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"291\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0443\u044e \u043f\u0440\u044f\u043c\u043e\u0439 r, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \u0410. \u0412\u0435\u043a\u0442\u043e\u0440\u043e\u043c, \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u043c \u043a \u044d\u0442\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0431\u0443\u0434\u0435\u0442 \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438, \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u043f\u0435\u0440\u0435\u0434 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u043e \u0432\u044b\u0440\u0430\u0436\u0430\u0435\u0442\u0441\u044f \u0432 \u0432\u0438\u0434\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fd3ff01a978525adb880475d0a0d304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(1,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0410 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0410, \u0412 \u0438 \u0421 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0441 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \u0435\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u043e\u0440\u043c\u0430\u043b\u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2278392c74541903e84c40636e7f639_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}=(1,4,-3) \\quad \\longrightarrow \\quad \\pi : \\ 1x+4y-3z+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"377\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u043e\u0447\u043a\u0430 \u0410 \u0434\u043e\u043b\u0436\u043d\u0430 \u043b\u0435\u0436\u0430\u0442\u044c \u0432 \u044d\u0442\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u0410 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 D: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10ddfecdcccda04ffbed3050c6ce5f8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(4,0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8659ebec73b4b105c79e577a0a7727ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4+4\\cdot 0-3\\cdot (-1)+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a74808d2c61fe33db5d803d5c2b4749c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4+3+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"109\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-959115729e795b196c018c3e5fe0d5b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"7+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"78\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ad9cd621146368bea5d81d84aa5d1b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D=-7\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439 ry, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \u0410, \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e36d9c18276dad2d9ada0417be32c1d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi : \\ x+4y-3z-7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"184\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u0417\u043d\u0430\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0440\u044f\u043c\u043e\u0439. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u043f\u0440\u044f\u043c\u043e\u0439 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u0440\u0435\u0448\u0430\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd611c8a6c7e516dbb67583b49f0b8e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}x=1 + t \\\\[1.7ex] y=5 +4t\\\\[1.7ex] z=-4-3t \\end{cases} \\qquad \\qquad \\pi : \\ x+4y-3z-7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"415\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7852fbe82935cb80948392ece78525bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1+t)+4(5+4t)-3(-4-3t)-7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"307\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-03bf61d8e06f77dcb88707b3825a8f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1+t+20+16t+12+9t-7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"261\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-94ed39e3d685ae2b03f269a9da7dd0a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"26t+26=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"96\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e99205a6c41b2ae65c560013b9aa1f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"26t=-26\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"80\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5d5cd7fed91a3e59d8059cb486d7fdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=\\cfrac{-26}{26}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"72\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35d11e298e261d1ee0e702c094322281_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u043b\u0438\u043d\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b0c515e3969169679e810db65a99e3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=-1 \\ \\longrightarrow \\ \\begin{cases}x=1 -1=0 \\\\[1.7ex] y=5 +4\\cdot (-1)=1\\\\[1.7ex] z=-4-3\\cdot (-1)=-1 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"299\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u044f\u043c\u043e\u0439 r \u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0439 \u0435\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d3c3451c553224af2b93bf9e49ba1ed6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"M(0,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0442\u043e\u0447\u043a\u0443, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0435 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 \u041c; \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u0443\u044e \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u044b: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4b39555d71f045dd42e9422dd077679_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} A' &amp; = 2M - A \\\\[2ex] &amp;= 2(0,1,-1) - (4,0,-1) \\\\[2ex] &amp; = (0,2,-2)-(4,0,-1)\\\\[2ex] &amp; = \\bm{(-4,2,-1)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"147\" width=\"211\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"punto-simetrico-respecto-a-un-plano\"><\/span> \u0442\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043c\u0435\u0442\u043e\u0434 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0432\u043e \u0435\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435:<\/p>\n<p> <strong>\u0422\u043e\u0447\u043a\u0430 \u0410&#8217; \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0435\u0441\u043b\u0438 \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438 \u0410&#8217; \u0438 \u0410 \u043b\u0435\u0436\u0430\u0442 \u043d\u0430 \u043e\u0434\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0438 \u043f\u0440\u0438 \u044d\u0442\u043e\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u043e\u0439 \u0410&#8217; \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044e \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u043e\u0439 \u0410 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e.<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/point-symetrique-d-un-autre-point-par-respect-d-un-plan.webp\" alt=\"\u0442\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438\" class=\"wp-image-2611\" width=\"402\" height=\"465\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-843280748c244e7f9c83ceda57c4c33e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,\\pi)= d(A',\\pi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u044e \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0442\u043e\u0447\u043a\u0430\u043c\u0438.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u03c0, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0448\u0430\u0433\u0438:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u041d\u0430\u0439\u0434\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \u0410. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043a \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">\u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439 (\u0442\u043e\u0447\u043a\u0430 \u041c \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0433\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f).<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">\u041c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0441\u0442\u0438 \u0442\u043e\u0447\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 (\u0441\u043c. \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u0440\u0430\u0437\u0434\u0435\u043b\u0430), \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u0442\u043e\u0447\u043a\u0438 A \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 M. \u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0438\u0441\u043a\u0430\u043b\u0438.<\/span> <\/li>\n<\/ol>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-determinar-el-punto-simetrico-respecto-a-un-plano\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u041d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u043d\u0443\u044e \u0437\u0430\u0434\u0430\u0447\u0443 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438:<\/p>\n<ul>\n<li> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 A \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u03c0. \u0421\u043a\u0430\u0437\u0430\u0432 \u0442\u043e\u0447\u043a\u0443 \u0438 \u043f\u043b\u0430\u043d:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-764c77ab01ff5f982839f6bc69b91162_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A(3,-4,2) \\qquad \\qquad \\pi: \\ 2x+y-z-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0435\u0440\u0432\u043e\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c, \u044d\u0442\u043e \u043d\u0430\u0439\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0438\u0438, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0440\u043e\u0445\u043e\u0434\u044f\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \u0410. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440 \u043d\u043e\u0440\u043c\u0430\u043b\u0438 \u043a \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043b\u0438\u043d\u0438\u0438, \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u043a\u043e\u0442\u043e\u0440\u043e\u0439 X, Y, Z \u2014 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043f\u0440\u0438 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0445 A, B \u0438 C \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-343ad7603e2777441731b82b5870295d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi: \\ 2x+y-z-6=0 \\quad \\longrightarrow \\quad \\vv{n} = (2,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"353\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0440\u044f\u043c\u043e\u0439, \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0441 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0438 \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0435\u0433\u043e \u0442\u043e\u0447\u0435\u043a (\u0442\u043e\u0447\u043a\u0438 \u0410):<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ec51a68802f626dcd5cf7a3bc1dda59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}x=3 + 2t \\\\[1.7ex] y=-4 +t\\\\[1.7ex] z=2-t \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"128\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0417\u043d\u0430\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0440\u044f\u043c\u043e\u0439, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u043f\u0440\u044f\u043c\u043e\u0439 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb4ee2c7f6742eec2e1fa11cac3c5635_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases}x=3 + 2t \\\\[1.7ex] y=-4 +t\\\\[1.7ex] z=2-t \\end{cases} \\qquad \\qquad \\pi : \\ 2x+y-z-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"397\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbd71a4094da61137e01c53f34de7058_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2(3+2t)+(-4+t)-(2-t)-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a6f4c7a9c5c5277b866385627b521bb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6+4t-4+t-2+t-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"226\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1360d3226af716e09f10a17743771dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6t-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"78\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a6bdb4ce652ce19b9ce2304834e1cb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6t=6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-90ecb612afe8f2bc45dd7111119b07a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=\\cfrac{6}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abf8f2abfdf1913d009a51ad64786690_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u043b\u0438\u043d\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a9373141f2f699971d5789e1cb0ed0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=1 \\ \\longrightarrow \\ \\begin{cases}x=3 + 2\\cdot 1 =5\\\\[1.7ex] y=-4 +1=-3\\\\[1.7ex] z=2-1=1 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"238\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418\u0442\u0430\u043a, \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0430 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1c91141b9bba6d3ffa4c81fc2d1ef446_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"M(5,-3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043d\u0430\u043c \u043f\u0440\u043e\u0441\u0442\u043e \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0442\u043e\u0447\u043a\u0443, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0435 \u0410 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0447\u043a\u0438 \u041c. \u0418 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u0443\u044e \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8199cf83bc3bdfbf0a7b2adb65a97af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} A' &amp; = 2M - A \\\\[2ex] &amp;= 2(5,-3,1) - (3,-4,2) \\\\[2ex] &amp; = (10,-6,2)-(3,-4,2)\\\\[2ex] &amp; = \\bm{(7,-2,0)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"147\" width=\"211\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0443 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u0422\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u041f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043c\u044b \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438: \u0422\u043e\u0447\u043a\u0430 \u0410&#8217; \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0410 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d1%81%d0%b8%d0%bc%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%87%d0%bd%d0%b0%d1%8f-%d1%82%d0%be%d1%87%d0%ba%d0%b0-%d1%83%d1%87%d0%b8%d1%82%d1%8b%d0%b2%d0%b0%d1%8f-%d0%b4%d1%80%d1%83%d0%b3%d1%83%d1%8e-%d1%82\/\"> <span class=\"screen-reader-text\">\u0422\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u043f\u0440\u044f\u043c\u043e\u0439 \u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[15],"tags":[],"class_list":["post-248","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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\u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u043e\u0447\u043a\u0438: \u0422\u043e\u0447\u043a\u0430 \u0410&#8217; \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0410 &hellip; \u0422\u043e\u0447\u043a\u0430, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 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