{"id":249,"date":"2023-07-10T13:40:44","date_gmt":"2023-07-10T13:40:44","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%86%d9%82%d8%b7%d8%a9-%d9%85%d8%aa%d9%86%d8%a7%d8%b8%d8%b1%d8%a9-%d9%85%d9%86-%d8%ae%d9%84%d8%a7%d9%84-%d8%a7%d8%ad%d8%aa%d8%b1%d8%a7%d9%85-%d9%86%d9%82%d8%b7%d8%a9-%d8%a3%d8%ae%d8%b1%d9%89-%d8%b9\/"},"modified":"2023-07-10T13:40:44","modified_gmt":"2023-07-10T13:40:44","slug":"%d9%86%d9%82%d8%b7%d8%a9-%d9%85%d8%aa%d9%86%d8%a7%d8%b8%d8%b1%d8%a9-%d9%85%d9%86-%d8%ae%d9%84%d8%a7%d9%84-%d8%a7%d8%ad%d8%aa%d8%b1%d8%a7%d9%85-%d9%86%d9%82%d8%b7%d8%a9-%d8%a3%d8%ae%d8%b1%d9%89-%d8%b9","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%86%d9%82%d8%b7%d8%a9-%d9%85%d8%aa%d9%86%d8%a7%d8%b8%d8%b1%d8%a9-%d9%85%d9%86-%d8%ae%d9%84%d8%a7%d9%84-%d8%a7%d8%ad%d8%aa%d8%b1%d8%a7%d9%85-%d9%86%d9%82%d8%b7%d8%a9-%d8%a3%d8%ae%d8%b1%d9%89-%d8%b9\/","title":{"rendered":"\u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649\u060c \u062e\u0637 \u0648\u0645\u0633\u062a\u0648\u0649"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649\u060c \u0648\u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u062e\u0637\u060c \u0648\u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"punto-simetrico-respecto-a-otro-punto\"><\/span> \u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0642\u0628\u0644 \u0623\u0646 \u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0627\u062c\u0639 \u0645\u0627 \u0647\u064a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0628\u0627\u0644\u0636\u0628\u0637 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0646\u0642\u0637\u0629 A&#8217; \u0647\u064a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 M \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0646\u0642\u0637\u0629 A&#8217; \u062a\u0642\u0639 \u0628\u0634\u0643\u0644 \u0645\u062a\u0645\u0627\u062b\u0644 \u0639\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 M \u0645\u062b\u0644 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 A \u0648M. \u0644\u0630\u0644\u0643\u060c M \u0647\u064a \u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0646\u062a\u0635\u0641 \u0644\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u0627\u0646 \u0623 \u0648 \u0623&#8217;.<\/strong> <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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=\"\u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649\" class=\"wp-image-2568\" width=\"224\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u0642\u0648\u0644 \u0623\u064a\u0636\u064b\u0627 \u0625\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 M \u0647\u064a \u0645\u0631\u0643\u0632 \u0627\u0644\u062a\u0645\u0627\u062b\u0644.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627\u060c \u0644\u062d\u0633\u0627\u0628 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644\u060c \u0633\u0648\u0641 \u0646\u0633\u062a\u062e\u062f\u0645 <a href=\"https:\/\/mathority.org\/ar\/\u0635\u064a\u063a\u0629-\u0644\u0646\u0642\u0637\u0629-\u0627\u0644\u0645\u0646\u062a\u0635\u0641-\u0644\u0645\u062a\u062c\u0647-\u0627\u0644\u0642\u0637\u0639\u0629\/\">\u0635\u064a\u063a\u0629 \u0646\u0642\u0637\u0629 \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0642\u0637\u0639\u0629<\/a> :<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0646\u0633\u062a\u062e\u0631\u062c \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062c\u0647\u0648\u0644\u0629 A&#8217; \u0648\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 <strong>\u0635\u064a\u063a\u0629 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649:<\/strong> <\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-el-punto-simetrico-respecto-a-otro-punto\"><\/span> \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0648\u0641 \u0646\u062d\u0633\u0628 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 M. \u062e\u0630 \u0628\u0639\u064a\u0646 \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0648\u0644\u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0628\u064a\u0646 \u0647\u0627\u062a\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646\u060c \u0646\u0637\u0628\u0642 \u0635\u064a\u063a\u0629 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0633\u062a\u0628\u062f\u0644 \u0627\u0644\u0646\u0642\u0627\u0637 \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0648\u0646\u0639\u0645\u0644: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"punto-simetrico-respecto-a-una-recta\"><\/span> \u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0644\u062e\u0637 \u0645\u0633\u062a\u0642\u064a\u0645<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0642\u062f \u0631\u0623\u064a\u0646\u0627 \u0644\u0644\u062a\u0648 \u0641\u0643\u0631\u0629 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649. \u062d\u0633\u0646\u064b\u0627\u060c \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0644\u0646\u0642\u0637\u0629 \u0645\u0627 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u062e\u0637 \u0645\u062a\u0634\u0627\u0628\u0647\u0629 \u062c\u062f\u064b\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0646\u0642\u0637\u0629 A&#8217; \u0647\u064a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u062e\u0637 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0646\u0642\u0637\u062a\u0627\u0646 A&#8217; \u0648 A&#8217; \u062a\u0642\u0639\u0627\u0646 \u0639\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u062e\u0637\u060c \u0648\u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 A&#8217; \u0648\u0627\u0644\u062e\u0637 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 A \u0648\u0627\u0644\u062e\u0637.<\/strong> <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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=\"\u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0645\u0646 \u0646\u0642\u0637\u0629 \u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u062e\u0637\" class=\"wp-image-2586\" width=\"470\" height=\"362\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627 \u0641\u0625\u0646 \u0627\u0644\u062e\u0637 <em>r<\/em> \u0647\u0648 \u0623\u064a\u0636\u064b\u0627 \u0645\u062d\u0648\u0631 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0627\u0637.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0644\u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u062a\u0646\u0627\u0638\u0631 \u0627\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0633\u062a\u0642\u064a\u0645 <em>r<\/em> \u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=;text-align:right;direction:rtl\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px;text-align:right;direction:rtl\"><span style=\"color:#000000;font-weight: normal;\">\u0646\u062c\u062f \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0645\u0639 \u0627\u0644\u062e\u0637 <em>r<\/em> \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0639\u0628\u0631 \u0627\u0644\u0646\u0642\u0637\u0629 A (\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u03c0 \u0645\u0646 \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0627\u0644\u0633\u0627\u0628\u0642). \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0639\u0644\u064a\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637\u060c \u0648\u0627\u0644\u0630\u064a \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0644\u0645\u0633\u062a\u0648\u0649.<\/span><\/li>\n<li style=\"margin-bottom:18px;text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0646\u062d\u0633\u0628 <a href=\"https:\/\/mathority.org\/ar\">\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0637\u0639<\/a> \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0645\u0648\u062c\u0648\u062f \u0648\u0627\u0644\u062e\u0637 (\u0627\u0644\u0646\u0642\u0637\u0629 M \u0641\u064a \u0627\u0644\u0635\u0648\u0631\u0629 \u0627\u0644\u0633\u0627\u0628\u0642\u0629).<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u062d\u0648\u0644 \u0627\u0644\u0646\u0642\u0637\u0629 (\u0627\u0644\u0645\u0648\u0636\u062d\u0629 \u0641\u064a \u0627\u0644\u0642\u0633\u0645 \u0623\u0639\u0644\u0627\u0647) \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 M. \u0648\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0647\u064a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u0627\u0644\u062a\u064a \u0643\u0646\u0627 \u0646\u0628\u062d\u062b \u0639\u0646\u0647\u0627.<\/span> <\/li>\n<\/ol>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-el-punto-simetrico-respecto-a-una-recta\"><\/span> \u0645\u062b\u0627\u0644 \u0644\u062d\u0633\u0627\u0628 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u062e\u0637<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0644\u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0645\u0633\u062a\u0642\u064a\u0645\u060c \u0633\u0646\u0631\u0649 \u062a\u0645\u0631\u064a\u0646\u064b\u0627 \u062a\u0645 \u062d\u0644\u0647 \u0643\u0645\u062b\u0627\u0644:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u062e\u0637 r. \u064a\u0642\u0627\u0644 \u0646\u0642\u0637\u0629 \u0648\u0633\u0637\u0631:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627\u064b\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 \u0627\u0644\u062e\u0637 r \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0639\u0628\u0631 \u0627\u0644\u0646\u0642\u0637\u0629 A. \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0644\u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0633\u064a\u0643\u0648\u0646 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637\u060c \u0648\u0645\u0643\u0648\u0646\u0627\u062a\u0647 \u0647\u064a \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0623\u0645\u0627\u0645 \u0627\u0644\u0645\u0639\u0644\u0645\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u0644\u0623\u0646\u0647 \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647\u0627 \u0641\u064a \u0634\u0643\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a A \u0648B \u0648C \u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u062a\u0637\u0627\u0628\u0642 \u0645\u0639 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0645\u062a\u062c\u0647\u0647\u0627 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u064a\u062c\u0628 \u0623\u0646 \u062a\u0642\u0639 \u0627\u0644\u0646\u0642\u0637\u0629 A \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0644\u0630\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0622\u0646 \u062a\u0639\u0648\u064a\u0636 \u0627\u0644\u0646\u0642\u0637\u0629 A \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0627\u0645\u0644 D: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 A \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0639\u0644\u064a\u0646\u0627 \u062d\u0633\u0627\u0628 \u0646\u0642\u0637\u0629 \u062a\u0642\u0627\u0637\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0639 \u0627\u0644\u062e\u0637. \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0646\u0639\u0648\u0636 \u0628\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u062e\u0637 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0646\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0646\u0627\u062a\u062c\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0633\u062a\u0628\u062f\u0644 \u0642\u064a\u0645\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0637\u0639 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 r \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0639\u0644\u064a\u0647 \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u064a\u0643\u0641\u064a \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 M\u061b \u0648\u0644\u0647\u0630\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0648\u0636\u062d\u0629 \u0641\u064a \u0628\u062f\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"punto-simetrico-respecto-a-un-plano\"><\/span> \u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0625\u0644\u0649 \u0627\u0644\u0637\u0627\u0626\u0631\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0642\u0628\u0644 \u0627\u0644\u0627\u0637\u0644\u0627\u0639 \u0639\u0644\u0649 \u0637\u0631\u064a\u0642\u0629 \u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u062a\u0645\u0627\u062b\u0644 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0645\u0627 \u0647\u0648 \u062a\u0639\u0631\u064a\u0641\u0647\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0646\u0642\u0637\u0629 A&#8217; \u0647\u064a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0646\u0642\u0637\u062a\u0627\u0646 A&#8217; \u0648 A \u062a\u0642\u0639\u0627\u0646 \u0639\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0648\u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 A&#8217; \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u062a\u0639\u0627\u062f\u0644 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 A \u0648\u0627\u0644\u0645\u0633\u062a\u0648\u0649.<\/strong> <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\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=\"\u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0637\u0627\u0626\u0631\u0629\" class=\"wp-image-2611\" width=\"402\" height=\"465\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646\u060c \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0647\u0648 \u0623\u064a\u0636\u064b\u0627 \u0645\u0633\u062a\u0648\u0649 \u062a\u0645\u0627\u062b\u0644 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u03c0\u060c \u0639\u0644\u064a\u0643 \u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=;text-align:right;direction:rtl\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px;text-align:right;direction:rtl\"><span style=\"color:#000000;font-weight: normal;\">\u0646\u062c\u062f \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 A. \u0648\u0644\u0647\u0630\u0627 \u0633\u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0628\u0627\u0639\u062a\u0628\u0627\u0631\u0647 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637.<\/span><\/li>\n<li style=\"margin-bottom:18px;text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0646\u062d\u0633\u0628 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0637\u0639 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0648\u062c\u0648\u062f (\u0627\u0644\u0646\u0642\u0637\u0629 M \u0641\u064a \u0627\u0644\u0635\u0648\u0631\u0629 \u0627\u0644\u0633\u0627\u0628\u0642\u0629).<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u062d\u0648\u0644 \u0627\u0644\u0646\u0642\u0637\u0629 (\u0627\u0644\u0645\u0648\u0636\u062d\u0629 \u0641\u064a \u0642\u0633\u0645 \u0627\u0644\u0628\u062f\u0627\u064a\u0629) \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 M. \u0648\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0647\u064a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u0627\u0644\u062a\u064a \u0643\u0646\u0627 \u0646\u0628\u062d\u062b \u0639\u0646\u0647\u0627.<\/span> <\/li>\n<\/ol>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-determinar-el-punto-simetrico-respecto-a-un-plano\"><\/span> \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646\u0643 \u0623\u062f\u0646\u0627\u0647 \u0631\u0624\u064a\u0629 \u0645\u0634\u0643\u0644\u0629 \u062a\u0645 \u062d\u0644\u0647\u0627 \u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0646\u0642\u0637\u0629 \u062a\u0646\u0627\u0638\u0631 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062a\u062d\u062f\u064a\u062f \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0644\u0640 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0633\u062a\u0648\u0649 \u03c0. \u0648\u0628\u0639\u062f \u0623\u0646 \u0642\u0644\u062a \u0627\u0644\u0646\u0642\u0637\u0629 \u0648\u0627\u0644\u062e\u0637\u0629:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644 \u0645\u0627 \u064a\u062a\u0639\u064a\u0646 \u0639\u0644\u064a\u0646\u0627 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0647 \u0647\u0648 \u0625\u064a\u062c\u0627\u062f \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 A. \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0639\u0645\u0648\u062f\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0628\u0627\u0639\u062a\u0628\u0627\u0631\u0647 \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0644\u062e\u0637 \u0627\u0644\u0630\u064a \u0645\u0643\u0648\u0646\u0627\u062a\u0647 X\u060c Y \u0648Z \u0647\u064a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f A \u0648B \u0648C \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a \u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0622\u0646 \u0625\u0646\u0634\u0627\u0621 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0627\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u062e\u0637 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f \u0645\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0645\u0639 \u0648\u062c\u0648\u062f \u0645\u062a\u062c\u0647 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0648\u0625\u062d\u062f\u0649 \u0646\u0642\u0627\u0637\u0647 (\u0627\u0644\u0646\u0642\u0637\u0629 A):<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u060c \u0646\u062d\u0633\u0628 \u0646\u0642\u0637\u0629 \u062a\u0642\u0627\u0637\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0648\u0627\u0644\u062e\u0637 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0644\u062a\u0639\u0648\u064a\u0636 \u0628\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u062e\u0637 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0633\u062a\u0628\u062f\u0644 \u0642\u064a\u0645\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062e\u0637:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0637\u0639 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u064a \u0648\u0627\u0644\u0645\u0633\u062a\u0642\u064a\u0645 \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062d\u062a\u0627\u062c \u0641\u0642\u0637 \u0625\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 A \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0646\u0642\u0637\u0629 M. \u0648\u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0648\u0636\u062d\u0629 \u0641\u064a \u0628\u062f\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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>\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649\u060c \u0648\u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u062e\u0637\u060c \u0648\u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. \u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649 \u0642\u0628\u0644 \u0623\u0646 \u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0627\u062c\u0639 \u0645\u0627 \u0647\u064a \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0628\u0627\u0644\u0636\u0628\u0637 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649: \u0627\u0644\u0646\u0642\u0637\u0629 A&#8217; &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%86%d9%82%d8%b7%d8%a9-%d9%85%d8%aa%d9%86%d8%a7%d8%b8%d8%b1%d8%a9-%d9%85%d9%86-%d8%ae%d9%84%d8%a7%d9%84-%d8%a7%d8%ad%d8%aa%d8%b1%d8%a7%d9%85-%d9%86%d9%82%d8%b7%d8%a9-%d8%a3%d8%ae%d8%b1%d9%89-%d8%b9\/\"> <span class=\"screen-reader-text\">\u0646\u0642\u0637\u0629 \u0645\u062a\u0646\u0627\u0638\u0631\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0646\u0642\u0637\u0629 \u0623\u062e\u0631\u0649\u060c \u062e\u0637 \u0648\u0645\u0633\u062a\u0648\u0649<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &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-249","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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