{"id":246,"date":"2023-07-10T13:40:44","date_gmt":"2023-07-10T13:40:44","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e7%9b%b4%e7%b7%9a%e4%b8%8a%e3%81%8a%e3%82%88%e3%81%b3%e5%bc%8f%e5%b9%b3%e9%9d%a2%e4%b8%8a%e3%81%ae%e5%88%a5%e3%81%ae%e7%82%b9%e3%82%92%e5%9f%ba%e6%ba%96%e3%81%ab%e3%81%97%e3%81%a6%e5%af%be%e7%a7%b0\/"},"modified":"2023-07-10T13:40:44","modified_gmt":"2023-07-10T13:40:44","slug":"%e7%9b%b4%e7%b7%9a%e4%b8%8a%e3%81%8a%e3%82%88%e3%81%b3%e5%bc%8f%e5%b9%b3%e9%9d%a2%e4%b8%8a%e3%81%ae%e5%88%a5%e3%81%ae%e7%82%b9%e3%82%92%e5%9f%ba%e6%ba%96%e3%81%ab%e3%81%97%e3%81%a6%e5%af%be%e7%a7%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e7%9b%b4%e7%b7%9a%e4%b8%8a%e3%81%8a%e3%82%88%e3%81%b3%e5%bc%8f%e5%b9%b3%e9%9d%a2%e4%b8%8a%e3%81%ae%e5%88%a5%e3%81%ae%e7%82%b9%e3%82%92%e5%9f%ba%e6%ba%96%e3%81%ab%e3%81%97%e3%81%a6%e5%af%be%e7%a7%b0\/","title":{"rendered":"\u4ed6\u306e\u70b9\u3001\u7dda\u3001\u9762\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u5225\u306e\u70b9\u3001\u7dda\u3001\u5e73\u9762\u306b\u5bfe\u3059\u308b\u5bfe\u79f0\u70b9\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4f8b\u984c\u3084\u6f14\u7fd2\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"punto-simetrico-respecto-a-otro-punto\"><\/span>\u5225\u306e\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5bfe\u79f0\u70b9\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u3092\u8aac\u660e\u3059\u308b\u524d\u306b\u3001\u5225\u306e\u70b9\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u70b9\u3068\u306f\u6b63\u78ba\u306b\u306f\u4f55\u306a\u306e\u304b\u3092\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u70b9 A&#8217; \u304c\u70b9 M \u304b\u3089\u70b9 A \u3068\u70b9 M \u306e\u9593\u306e\u8ddd\u96e2\u3068\u540c\u3058\u8ddd\u96e2\u306b\u5bfe\u79f0\u7684\u306b\u4f4d\u7f6e\u3059\u308b\u5834\u5408\u3001\u70b9 A&#8217; \u306f\u5225\u306e\u70b9 M \u306b\u95a2\u3057\u3066\u70b9 A \u306e\u5bfe\u79f0\u70b9\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001M \u306f\u6b21\u306e\u5f0f\u3067\u5f62\u6210\u3055\u308c\u308b\u7dda\u5206\u306e\u4e2d\u70b9\u3067\u3059\u3002\u70b9A\u3068A&#8217;\u3002<\/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=\"\u5225\u306e\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9\" 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>\u4e00\u65b9\u3067\u3001\u70b9 M \u304c\u5bfe\u79f0\u306e\u4e2d\u5fc3\u3067\u3042\u308b\u3068\u3082\u8a00\u3044\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5bfe\u79f0\u70b9\u306e\u5ea7\u6a19\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001<a href=\"https:\/\/mathority.org\/ja\/\u30bb\u30af\u3099\u30e1\u30f3\u30c8\u30d8\u3099\u30af\u30c8\u30eb\u306e\u4e2d\u70b9\u306e\u516c\u5f0f\/\">\u30bb\u30b0\u30e1\u30f3\u30c8\u306e\u4e2d\u70b9\u306e\u516c\u5f0f<\/a>\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/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>\u3053\u306e\u65b9\u7a0b\u5f0f\u304b\u3089\u672a\u77e5\u306e\u70b9 A&#8217; \u3092\u62bd\u51fa\u3057\u3001<strong>\u5225\u306e\u70b9\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u306e\u516c\u5f0f\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002<\/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>\u4ed6\u306e\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u3092\u6c42\u3081\u308b\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4f8b\u3068\u3057\u3066\u3001\u70b9 M \u306b\u5bfe\u3059\u308b\u70b9 A \u306e\u5bfe\u79f0\u70b9\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u6b21\u306e 2 \u3064\u306e\u70b9\u3092\u8003\u616e\u3057\u307e\u3059\u3002<\/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>\u3053\u308c\u3089 2 \u3064\u306e\u70b9\u9593\u306e\u5bfe\u79f0\u70b9\u3092\u6c7a\u5b9a\u3059\u308b\u306b\u306f\u3001\u5225\u306e\u70b9\u306b\u95a2\u3059\u308b\u5bfe\u79f0\u70b9\u306e\u516c\u5f0f\u3092\u9069\u7528\u3057\u307e\u3059\u3002<\/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>\u3053\u3053\u3067\u3001\u5f0f\u5185\u306e\u70b9\u3092\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/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>\u305d\u3057\u3066\u79c1\u305f\u3061\u306f\u4ee5\u4e0b\u306e\u3053\u3068\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002 <\/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>\u76f4\u7dda\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5225\u306e\u70b9\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u306e\u6982\u5ff5\u3092\u898b\u3066\u304d\u307e\u3057\u305f\u3002\u3055\u3066\u3001\u7dda\u306b\u5bfe\u3059\u308b\u70b9\u306e\u5bfe\u79f0\u70b9\u306f\u975e\u5e38\u306b\u3088\u304f\u4f3c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><strong>\u70b9A&#8217;\u306f\u30012\u3064\u306e\u70b9A&#8217;\u3068A\u304c\u76f4\u7dda\u306b\u5782\u76f4\u306a\u540c\u4e00\u76f4\u7dda\u4e0a\u306b\u3042\u308a\u3001\u3055\u3089\u306b\u3001\u70b9A&#8217;\u3068\u76f4\u7dda\u306e\u9593\u306e\u8ddd\u96e2\u304c\u8ddd\u96e2\u306b\u7b49\u3057\u3044\u5834\u5408\u3001\u70b9A\u306e\u7dda\u5bfe\u79f0\u306a\u70b9\u3067\u3059\u3002\u70b9A\u3068\u76f4\u7dda\u306e\u9593\u3002<\/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=\"\u7dda\u306b\u5bfe\u3057\u3066\u70b9\u306e\u5bfe\u79f0\u70b9\" 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>\u3057\u305f\u304c\u3063\u3066\u3001\u7dda<em>r \u306f<\/em>\u70b9\u9593\u306e\u5bfe\u79f0\u8ef8\u3067\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u7dda<em>r<\/em>\u306b\u5bfe\u3059\u308b\u70b9 A \u306e\u5bfe\u79f0\u70b9\u3092\u6c7a\u5b9a\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u624b\u9806\u306b\u5f93\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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;\">\u70b9 A \u3092\u901a\u904e\u3059\u308b\u7dda<em>r<\/em>\u306b\u5782\u76f4\u306a\u5e73\u9762 (\u524d\u306e\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u8868\u73fe\u306e\u5e73\u9762 \u03c0) \u3092\u898b\u3064\u3051\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308b\u7dda\u306e\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u898b\u3064\u304b\u3063\u305f\u5e73\u9762\u3068\u76f4\u7dda\u3068\u306e<a href=\"https:\/\/mathority.org\/ja\">\u4ea4\u70b9<\/a>(\u524d\u306e\u753b\u50cf\u306e\u70b9 M) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u70b9\u306b\u95a2\u3059\u308b\u5bfe\u79f0\u70b9\u306e\u5f0f (\u4e0a\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u53c2\u7167) \u3092\u4f7f\u7528\u3057\u3066\u3001\u70b9 M \u306b\u5bfe\u3059\u308b\u70b9 A \u306e\u5bfe\u79f0\u70b9\u3092\u898b\u3064\u3051\u307e\u3059\u3002\u7d50\u679c\u306f\u3001\u63a2\u3057\u3066\u3044\u305f\u5bfe\u79f0\u70b9\u3067\u3059\u3002<\/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>\u7dda\u5bfe\u79f0\u70b9\u306e\u8a08\u7b97\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7dda\u306b\u5bfe\u3059\u308b\u5225\u306e\u70b9\u306e\u5bfe\u79f0\u70b9\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u304c\u308f\u304b\u3063\u305f\u3089\u3001\u4f8b\u3068\u3057\u3066\u6f14\u7fd2\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u76f4\u7ddar\u306b\u95a2\u3057\u3066\u70b9A\u306e\u5bfe\u79f0\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002\u70b9\u3068\u7dda\u3067\u3053\u3046\u8a00\u308f\u308c\u307e\u3059\u3002<\/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>\u307e\u305a\u3001\u70b9 A \u3092\u901a\u308b\u76f4\u7dda r \u306b\u5782\u76f4\u306a\u5e73\u9762\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u304c\u76f4\u7dda\u306e\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308a\u3001\u305d\u306e\u6210\u5206\u304c\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u524d\u306e\u9805\u306b\u306a\u308a\u307e\u3059\u3002<\/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>\u305d\u308c\u306f\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u65b9\u7a0b\u5f0f\u306e\u5f62\u5f0f\u3067\u8868\u73fe\u3055\u308c\u308b\u305f\u3081\u3067\u3059\u3002<\/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>\u305d\u3057\u3066\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570 A\u3001B\u3001C \u306f\u305d\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19\u3068\u4e00\u81f4\u3059\u308b\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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>\u70b9 A \u306f\u3053\u306e\u5e73\u9762\u4e0a\u306b\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u70b9 A \u3092\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u4fc2\u6570 D \u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/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>\u3057\u305f\u304c\u3063\u3066\u3001\u70b9 A \u3092\u901a\u308b\u76f4\u7dda ry \u306b\u5782\u76f4\u306a\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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>\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u304c\u308f\u304b\u3063\u305f\u3089\u3001\u5e73\u9762\u3068\u76f4\u7dda\u306e\u4ea4\u70b9\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u7dda\u306e\u5ea7\u6a19\u3092\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306b\u4ee3\u5165\u3057\u3001\u7d50\u679c\u3068\u3057\u3066\u5f97\u3089\u308c\u308b\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u307e\u3059\u3002 <\/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>\u3053\u3053\u3067\u3001\u6b21\u306e\u5024\u3092\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/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>\u6b21\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3067\u5f97\u3089\u308c\u307e\u3059\u3002<\/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>\u3057\u305f\u304c\u3063\u3066\u3001\u7dda r \u3068\u305d\u308c\u306b\u5782\u76f4\u306a\u5e73\u9762\u3068\u306e\u4ea4\u70b9\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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>\u6700\u5f8c\u306b\u3001\u70b9 M \u306b\u95a2\u3057\u3066\u70b9 A \u306e\u5bfe\u79f0\u70b9\u3092\u898b\u3064\u3051\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002\u3053\u306e\u305f\u3081\u306b\u306f\u3001\u3053\u306e\u30da\u30fc\u30b8\u306e\u5192\u982d\u306b\u3042\u308b\u5f0f\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 <\/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>\u5e73\u9762\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5e73\u9762\u306b\u5bfe\u3059\u308b\u5225\u306e\u70b9\u306e\u5bfe\u79f0\u70b9\u3092\u6c7a\u5b9a\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3059\u308b\u524d\u306b\u3001\u305d\u306e\u5b9a\u7fa9\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u70b9A&#8217;\u306f\u30012\u3064\u306e\u70b9A&#8217;\u3068A\u304c\u5e73\u9762\u306b\u5782\u76f4\u306a\u540c\u4e00\u7dda\u4e0a\u306b\u3042\u308a\u3001\u304b\u3064\u3001\u70b9A&#8217;\u3068\u5e73\u9762\u306e\u9593\u306e\u8ddd\u96e2\u304c\u8ddd\u96e2\u306b\u7b49\u3057\u3044\u5834\u5408\u3001\u70b9A\u306e\u5bfe\u79f0\u70b9\u3067\u3059\u3002\u70b9A\u3068\u5e73\u9762\u306e\u9593\u3002<\/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=\"\u5e73\u9762\u306b\u5bfe\u3057\u3066\u5225\u306e\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9\" 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>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u5e73\u9762\u306f 2 \u70b9\u9593\u306e\u5bfe\u79f0\u9762\u3067\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u9762 \u03c0 \u306b\u95a2\u3057\u3066\u70b9 A \u306e\u5bfe\u79f0\u70b9\u306e\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u3092\u77e5\u308b\u306b\u306f\u3001\u6b21\u306e\u624b\u9806\u306b\u5f93\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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;\">\u70b9 A \u3092\u901a\u308b\u5e73\u9762\u306b\u5782\u76f4\u306a\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u306b\u3001\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u3092\u7dda\u306e\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u5e73\u9762\u3068\u898b\u3064\u304b\u3063\u305f\u7dda\u3068\u306e\u4ea4\u70b9 (\u524d\u306e\u753b\u50cf\u306e\u70b9 M) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u70b9\u306b\u95a2\u3059\u308b\u5bfe\u79f0\u70b9\u306e\u5f0f (\u6700\u521d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u793a\u3057\u305f) \u3092\u4f7f\u7528\u3057\u3066\u3001\u70b9 M \u306b\u5bfe\u3059\u308b\u70b9 A \u306e\u5bfe\u79f0\u70b9\u3092\u898b\u3064\u3051\u307e\u3059\u3002\u7d50\u679c\u306f\u3001\u63a2\u3057\u3066\u3044\u305f\u5bfe\u79f0\u70b9\u3067\u3059\u3002<\/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>\u5e73\u9762\u306b\u5bfe\u3059\u308b\u5bfe\u79f0\u70b9\u306e\u6c7a\u5b9a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4ee5\u4e0b\u306b\u3001\u5e73\u9762\u306b\u5bfe\u3059\u308b\u5225\u306e\u70b9\u306e\u5bfe\u79f0\u70b9\u306b\u95a2\u3059\u308b\u89e3\u6c7a\u6e08\u307f\u306e\u554f\u984c\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5e73\u9762 \u03c0 \u306b\u5bfe\u3059\u308b A \u306e\u5bfe\u79f0\u70b9\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002\u8981\u70b9\u3068\u8a08\u753b\u3092\u8ff0\u3079\u305f\u4e0a\u3067\u3001\u6b21\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/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>\u6700\u521d\u306b\u884c\u3046\u5fc5\u8981\u304c\u3042\u308b\u306e\u306f\u3001\u70b9 A \u3092\u901a\u308b\u5e73\u9762\u306b\u5782\u76f4\u306a\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u3092\u7dda\u306e\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u6210\u5206 X\u3001 Y\u3001Z \u306f\u305d\u308c\u305e\u308c\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306e\u9805 A\u3001B\u3001\u304a\u3088\u3073 C \u306e\u4fc2\u6570\u3067\u3059\u3002<\/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>\u3053\u308c\u3067\u3001\u898b\u3064\u304b\u3063\u305f\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3068\u305d\u306e\u70b9 (\u70b9 A) \u306e 1 \u3064\u3092\u4f7f\u7528\u3057\u3066\u3001\u5e73\u9762\u306b\u76f4\u4ea4\u3059\u308b\u76f4\u7dda\u306e\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u65b9\u7a0b\u5f0f\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002<\/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>\u5782\u7dda\u304c\u308f\u304b\u3063\u305f\u3089\u3001\u76f4\u7dda\u306e\u5ea7\u6a19\u3092\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u3001\u5e73\u9762\u3068\u76f4\u7dda\u306e\u4ea4\u70b9\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/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>\u3053\u3053\u3067\u3001\u6b21\u306e\u5024\u3092\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/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>\u6b21\u306e\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3067\u5f97\u3089\u308c\u307e\u3059\u3002<\/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>\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u9762\u3068\u5782\u7dda\u306e\u4ea4\u70b9\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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>\u6700\u5f8c\u306b\u3001\u70b9 M \u306b\u95a2\u3057\u3066\u70b9 A \u306e\u5bfe\u79f0\u70b9\u3092\u898b\u3064\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u3053\u306e\u30da\u30fc\u30b8\u306e\u5192\u982d\u306b\u3042\u308b\u516c\u5f0f\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/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>\u3053\u3053\u3067\u306f\u3001\u5225\u306e\u70b9\u3001\u7dda\u3001\u5e73\u9762\u306b\u5bfe\u3059\u308b\u5bfe\u79f0\u70b9\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4f8b\u984c\u3084\u6f14\u7fd2\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5225\u306e\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9 \u5bfe\u79f0\u70b9\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u3092\u8aac\u660e\u3059\u308b\u524d\u306b\u3001\u5225\u306e\u70b9\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u70b9\u3068\u306f\u6b63\u78ba\u306b\u306f &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e7%9b%b4%e7%b7%9a%e4%b8%8a%e3%81%8a%e3%82%88%e3%81%b3%e5%bc%8f%e5%b9%b3%e9%9d%a2%e4%b8%8a%e3%81%ae%e5%88%a5%e3%81%ae%e7%82%b9%e3%82%92%e5%9f%ba%e6%ba%96%e3%81%ab%e3%81%97%e3%81%a6%e5%af%be%e7%a7%b0\/\"> <span class=\"screen-reader-text\">\u4ed6\u306e\u70b9\u3001\u7dda\u3001\u9762\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9<\/span> \u3082\u3063\u3068\u8aad\u3080 &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-246","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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