{"id":269,"date":"2023-07-10T01:42:26","date_gmt":"2023-07-10T01:42:26","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%b8%a4%e7%82%b9%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%87%a0%e4%bd%95%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-10T01:42:26","modified_gmt":"2023-07-10T01:42:26","slug":"%e4%b8%a4%e7%82%b9%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%87%a0%e4%bd%95%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%b8%a4%e7%82%b9%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%87%a0%e4%bd%95%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\uff08\u51e0\u4f55\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u51e0\u4f55\u4e2d\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09\u3002\u60a8\u8fd8\u53ef\u4ee5\u67e5\u770b\u793a\u4f8b\uff0c\u6b64\u5916\u8fd8\u53ef\u4ee5\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u4e24\u70b9\u4e4b\u95f4\u8ddd\u79bb\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-formula-de-la-distancia-entre-dos-puntos\"><\/span>\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7b49\u4e8e\u8fde\u63a5\u5b83\u4eec\u7684\u7ebf\u6bb5\u7684\u957f\u5ea6\u3002\u56e0\u6b64\uff0c\u5728\u6570\u5b66\u4e2d\uff0c\u8981\u786e\u5b9a\u4e24\u4e2a\u4e0d\u540c\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u5fc5\u987b\u8ba1\u7b97\u5b83\u4eec\u7684\u5750\u6807\u5dee\u7684\u5e73\u65b9\uff0c\u7136\u540e\u6c42\u5e73\u65b9\u548c\u7684\u6839\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u7528\u4e8e\u8ba1\u7b97\u7b1b\u5361\u5c14\u5e73\u9762\u4e0a\u4e24\u4e2a\u4e0d\u540c\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u516c\u5f0f\u5982\u4e0b\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u8003\u8651\u4e24\u4e2a\u4e0d\u540c\u70b9\u7684\u5750\u6807\uff1a<\/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-617b8c4c3becdf6f6f5ee619a5c8e9d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x_1,y_1) \\qquad \\qquad B(x_2,y_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"><strong>\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u516c\u5f0f<\/strong>\u4e3a\uff1a<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u8fd9\u4e2a\u516c\u5f0f\u6765\u81ea\u4e8e\u5411\u91cf\u7684\u5927\u5c0f\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u7528\u8fd9\u4e2a\u516c\u5f0f\u6240\u505a\u7684\u5b9e\u9645\u4e0a\u662f\u8ba1\u7b97\u7531\u6240\u8ba8\u8bba\u7684\u4e24\u4e2a\u70b9\u786e\u5b9a\u7684\u5411\u91cf\u7684\u5927\u5c0f\u3002\u60a8\u53ef\u4ee5\u5728<a href=\"https:\/\/mathority.org\/cn\/\u5411\u91cf\u516c\u5f0f\u7684\u6a21\u793a\u4f8b\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u5411\u91cf\u6a21\u6570\u7684<\/a>\u89e3\u91ca\u4e2d\u9605\u8bfb\u66f4\u591a\u76f8\u5173\u5185\u5bb9\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\u7684\u6f14\u793a\u4e5f\u53ef\u4ee5\u4f7f\u7528\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406\u6765\u5b8c\u6210\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-geometrique-distance-entre-deux-points.webp\" alt=\"\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\" class=\"wp-image-5012\" width=\"329\" height=\"329\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p>\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406\u6307\u51fa\uff0c\u76f4\u89d2\u4e09\u89d2\u5f62\u659c\u8fb9\u7684\u5e73\u65b9\u7b49\u4e8e\u5176\u76f4\u89d2\u8fb9\u7684\u5e73\u65b9\u548c\uff0c\u56e0\u6b64\uff1a<\/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-a030628d3e6320afdcc61fd4c3100ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl(d(A,B)\\bigr)^2 = (x_2-x_1)^2 + (y_2-y_1)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"280\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u8981\u83b7\u5f97\u516c\u5f0f\uff0c\u60a8\u53ea\u9700\u627e\u5230\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5982\u679c\u6211\u4eec\u4f7f\u7528 3 \u5750\u6807\u70b9\uff0c\u7a7a\u95f4\u4e2d\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u5728 R3 \u4e2d\uff09\u7684\u516c\u5f0f\u5c06\u662f\u76f8\u540c\u7684\uff0c\u4f46\u6dfb\u52a0\u4e86 Z \u5750\u6807\uff1a <\/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-236a06c21ada3a9557cf73a29f47d8e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"374\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-distancia-entre-dos-puntos\"><\/span>\u8ba1\u7b97\u4e24\u70b9\u4e4b\u95f4\u8ddd\u79bb\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u4e24\u70b9\u4e4b\u95f4\u8ddd\u79bb\u516c\u5f0f\u7684\u5b9a\u4e49\uff0c\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5982\u4f55\u4f7f\u7528\u793a\u4f8b\u6765\u786e\u5b9a\u6240\u8ff0\u8ddd\u79bb\uff1a<\/p>\n<ul>\n<li>\u6c42\u4ee5\u4e0b\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a<\/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-cdf7bd1545cb6d04a4bb3851c6794466_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(-1,7) \\qquad \\qquad B(3,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"190\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u4ee5\u51e0\u4f55\u65b9\u5f0f\u6c42\u51fa\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u53ea\u9700\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5c06\u70b9\u7684\u5750\u6807\u4ee3\u5165\u516c\u5f0f\uff1a<\/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-02a4310cdfe1552b81816867261a17fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(3-(-1))^2+(4-7)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"271\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u8fdb\u884c\u8ba1\u7b97\uff1a<\/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-4e48600907e65f89fb9be0d55a2d3b3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} d(A,B)  &amp;= \\sqrt{(3+1)^2+(4-7)^2 \\vphantom{\\frac{1}{2}}} \\\\[2ex] &amp;= \\sqrt{4^2+(-3)^2 \\vphantom{\\frac{1}{2}}} \\\\[2ex] &amp;= \\sqrt{16+9}\\\\[2ex] &amp;= \\sqrt{25}\\\\[2ex] &amp; = \\bm{5}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"233\" width=\"244\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7b49\u4e8e 5 \u4e2a\u5355\u4f4d\u3002<\/p>\n<p>\u663e\u7136\uff0c\u8ddd\u79bb\u503c\u5fc5\u987b\u59cb\u7ec8\u4e3a\u6b63\u53f7\uff0c\u56e0\u4e3a\u8ddd\u79bb\u59cb\u7ec8\u4e3a\u6b63\u3002\u5426\u5219\uff0c\u5c31\u8bf4\u660e\u6211\u4eec\u5728\u67d0\u4e2a\u6b65\u9aa4\u4e0a\u72af\u4e86\u9519\u8bef\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-distancia-entre-dos-puntos\"><\/span>\u89e3\u51b3\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-aa5be81901d5be989c5b72facdd42354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(4,2) \\qquad \\qquad B(1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"177\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u627e\u5230\u4e24\u70b9\u4e4b\u95f4\u7684\u51e0\u4f55\u8ddd\u79bb\uff0c\u53ea\u9700\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u70b9\u7684\u5750\u6807\u4ee3\u5165\u516c\u5f0f\uff1a<\/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-4afec52bf1fdc3c32a004a86e312b164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(1-4)^2+(5-2)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"244\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8fdb\u884c\u8ba1\u7b97\uff1a <\/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-81d70676cabdc2985f2ebe7b88c54e2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} d(A,B) &amp; = \\sqrt{(-3)^2+3^2 } \\\\[2ex] &amp; = \\sqrt{9+9 } \\\\[2ex] &amp; = \\bm{\\sqrt{18}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"183\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u6c42\u4ee5\u4e0b\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-9b2fed9d7325f254ded1553b488d7a0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(8,6) \\qquad \\qquad B(-4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"190\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u627e\u5230\u4e24\u70b9\u4e4b\u95f4\u7684\u6570\u5b66\u8ddd\u79bb\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u76f8\u5e94\u7684\u516c\u5f0f\uff1a<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5c06\u70b9\u7684\u5750\u6807\u4ee3\u5165\u516c\u5f0f\uff1a<\/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-5d1814bdae0e934c17e4d699ba2223c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(-4-8)^2+(1-6)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"258\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8fdb\u884c\u8ba1\u7b97\uff1a <\/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-1c9f9f5c93377868a352891d5b09630a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} d(A,B)  &amp;= \\sqrt{(-12)^2+(-5)^2 } \\\\[2ex] &amp;= \\sqrt{144+25 }\\\\[2ex] &amp;= \\sqrt{169} \\\\[2ex] &amp;= \\bm{13}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"149\" width=\"219\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u8ba1\u7b97\u7531 A\u3001B\u3001C \u70b9\u5f62\u6210\u7684\u4e09\u89d2\u5f62\u7684\u5468\u957f\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a <\/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\/exercice-resolu-de-distance-entre-deux-points.webp\" alt=\"\u89e3\u51b3\u4e86\u4e24\u70b9\u4e4b\u95f4\u8ddd\u79bb\u7684\u7ec3\u4e60\" class=\"wp-image-3913\" width=\"338\" height=\"267\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u786e\u5b9a\u56fe\u8868\u4e0a\u6bcf\u4e2a\u70b9\u7684 X \u548c Y \u5750\u6807\uff1a <\/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-9a16d799fdc0fa3c371c35ba5f0f3a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" 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-df310f6e38e3e91250838800e5366e54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(4,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" 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-68d3d057862c60995dc725a90e942df4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(6,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u6240\u6709\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-1854b638ed0238a7b80632324e67ae0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(4-2)^2+(4-1)^2 } = \\sqrt{4+9} =\\sqrt{13} = 3,61\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"435\" style=\"vertical-align: -6px;\"><\/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-741fa87cdc51782a0770cd384048b8fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,C) = \\sqrt{(6-2)^2+(2-1)^2 } = \\sqrt{16+1} =\\sqrt{17} = 4,12\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"443\" style=\"vertical-align: -6px;\"><\/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-79954ecf2f51f8c6e230b15c56dfd2f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(B,C) = \\sqrt{(6-4)^2+(2-4)^2 } = \\sqrt{4+4} =\\sqrt{8} = 2,83\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"427\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u4e09\u89d2\u5f62\u7684\u5468\u957f\u5c31\u662f 3 \u6761\u8fb9\u7684\u957f\u5ea6\u4e4b\u548c\uff1a <\/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-9cdb85214a73df4e8a7e7ee238c1bc55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P=3,61+4,12+2,83= \\bm{10,56}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"251\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u68c0\u67e5\u4ee5 A\u3001B\u3001C \u70b9\u4e3a\u9876\u70b9\u7684\u4e09\u89d2\u5f62\u662f\u5426\u4e3a\u7b49\u8170\u4e09\u89d2\u5f62\u3002\u4f46\u4e09\u70b9\uff1a <\/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-df719532b223037ad6a672c50a294c3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(-4,5) \\qquad B(7,-5) \\qquad C(10,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"266\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u4f7f\u4e09\u89d2\u5f62\u6210\u4e3a\u7b49\u8170\u4e09\u89d2\u5f62\uff0c\u5b83\u7684\u4e24\u6761\u8fb9\u5fc5\u987b\u76f8\u7b49\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u627e\u5230\u5176\u6bcf\u6761\u8fb9\u7684\u957f\u5ea6\uff0c\u8be5\u957f\u5ea6\u5bf9\u5e94\u4e8e\u5176\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u4e09\u89d2\u5f62\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a <\/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-786e56f8fe183e8143b1fb4f7f616226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(7-(-4))^2+(-5-5)^2 } = \\sqrt{11^2+(-10)^2} = \\sqrt{221}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"492\" style=\"vertical-align: -6px;\"><\/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-61cea14c48c09e4b4ae79b45d78cb746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,C) = \\sqrt{(10-(-4))^2+(0-5)^2 } = \\sqrt{14^2+(-5)^2}  = \\sqrt{221}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"477\" style=\"vertical-align: -6px;\"><\/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-008513f83c089a4f9d4bc62b48a02aae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(B,C) = \\sqrt{(10-7)^2+(0-(-5))^2} = \\sqrt{3^2+5^2} = \\sqrt{34}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"430\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e09\u89d2\u5f62\u6709\u4e24\u6761\u76f8\u540c\u7684\u8fb9\uff0c\u7b2c\u4e09\u6761\u8fb9\u7684\u5c3a\u5bf8\u4e0e\u5176\u4ed6\u4e24\u6761\u8fb9\u4e0d\u540c\uff0c\u90a3\u4e48\u5b83\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u7b49\u8170\u4e09\u89d2\u5f62\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u5728 Y \u8f74\u4e0a\u627e\u5230\u4e0e\u4ee5\u4e0b\u4e24\u70b9\u7b49\u8ddd\u7684\u70b9\uff1a <\/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-94ff2ed3e9145831e9919ad74a4d4c4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(5,-3) \\qquad \\qquad B(-2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"204\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u5982\u679c\u8be5\u70b9\u4f4d\u4e8e\u8ba1\u7b97\u673a\u8f74\uff08OY \u8f74\uff09\u4e0a\uff0c\u5219\u610f\u5473\u7740\u8be5\u70b9\u7684\u6a2a\u5750\u6807\u4e3a\u96f6\uff1a<\/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-5cde05cd2f5f74f5290621fdbe275415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u6b21\uff0c\u5982\u679c\u8be5\u70b9\u4e0e\u70b9 A \u548c B \u7b49\u8ddd\uff0c\u5219\u610f\u5473\u7740\u6ee1\u8db3\u4ee5\u4e0b\u65b9\u7a0b\uff1a<\/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-26224760f49fac42cea9d39dfe53dd4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,A)= d(P,B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4f7f\u7528\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u524d\u9762\u7684\u65b9\u7a0b\u4e2d\u627e\u5230\u53d8\u91cf<em>y<\/em>\u7684\u503c\uff1a<\/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-8a5f1368ddd79fe90319f21cc904d392_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{(5-0)^2+(-3-y)^2 \\vphantom{\\frac{1}{2}}}=\\sqrt{(-2-0)^2+(4-y)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"374\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u65b9\u7a0b\u4e24\u8fb9\u90fd\u6709\u6839\uff0c\u6211\u4eec\u53ef\u4ee5\u5316\u7b80\uff1a<\/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-26c1085f06beb112f73bac79ec7a7a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5^2+(-3-y)^2=(-2)^2+(4-y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"264\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u89e3\u51b3\u663e\u7740\u7684\u5e42\u548c\u7b49\u5f0f\uff08\u6216\u663e\u7740\u7684\u4e58\u79ef\uff09\uff1a<\/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-59f4cfbad3f47e15ec8dd45d8eff5b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"25+9+y^2+6y=4+16+y^2-8y\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"277\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8fdb\u884c\u64cd\u4f5c\uff0c\u76f4\u5230\u627e\u5230\u672a\u77e5<em>y<\/em>\u7684\u503c\uff1a <\/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-1e112c8e3a8ff239195ad850bd0e3f55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2+6y-y^2+8y=4+16-25-9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"277\" style=\"vertical-align: -4px;\"><\/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-dc1582050e8015be81566a4ba06585ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"14y=-14\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/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-67e3c61051e1e6f4d5ae83c0a7f8f51a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-14}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"75\" 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-9f371b4e77462e28d9f6119571c92982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7b80\u800c\u8a00\u4e4b\uff0c\u95ee\u9898\u9648\u8ff0\u95ee\u6211\u4eec\u7684\u8981\u70b9\u662f\uff1a <\/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-5d1dd065d80d8fce8e53869201ad7b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P(0,-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p>\u5982\u679c\u60a8\u53d1\u73b0\u672c\u6587\u6709\u7528\uff0c\u60a8\u53ef\u80fd\u8fd8\u4f1a<a 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