{"id":233,"date":"2023-07-10T19:30:40","date_gmt":"2023-07-10T19:30:40","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%82%b9%e4%b8%8e%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0%e7%a4%ba%e4%be%8b\/"},"modified":"2023-07-10T19:30:40","modified_gmt":"2023-07-10T19:30:40","slug":"%e7%82%b9%e4%b8%8e%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0%e7%a4%ba%e4%be%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%82%b9%e4%b8%8e%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0%e7%a4%ba%e4%be%8b\/","title":{"rendered":"\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u7528\u4e8e\u8ba1\u7b97\u70b9\u548c\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\u516c\u5f0f\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4e00\u4e9b\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\u7ec3\u4e60\uff0c\u751a\u81f3\u8be5\u64cd\u4f5c\u7684\u5e94\u7528\u7a0b\u5e8f\uff08\u4f8b\u5982\uff0c\u8ba1\u7b97\u5e73\u884c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff09\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=\"formula-de-la-distancia-entre-un-punto-y-una-recta\"><\/span>\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u70b9\u5230\u7ebf\u7684\u8ddd\u79bb<\/strong>\u662f\u8be5\u70b9\u5230\u7ebf\u7684\u6700\u77ed\u8ddd\u79bb\u3002\u4ece\u6570\u5b66\u4e0a\u8bb2\uff0c\u8fd9\u4e2a\u6700\u5c0f\u8ddd\u79bb\u76f8\u5f53\u4e8e\u4ece\u8be5\u70b9\u5230\u8be5\u7ebf\u6240\u753b\u7684\u5782\u76f4\u4e8e\u8be5\u7ebf\u7684\u7ebf\u6bb5\u7684\u957f\u5ea6\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/distance-entre-un-point-et-une-droite-1.webp\" alt=\"\u70b9\u548c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u662f\u591a\u5c11\" class=\"wp-image-1951\" width=\"326\" height=\"291\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u70b9\u548c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u51e0\u4f55\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u7528\u4e8e\u8ba1\u7b97\u6240\u8ff0\u8ddd\u79bb\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\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\">\u7ed9\u5b9a\u76f4\u7ebf\u7684\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u548c\u5e73\u9762\u4e0a\u4efb\u610f\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-127fb199bd8a31769e3814d2581888eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ Ax+By+C=0 \\qquad \\qquad P(p_x,p_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"306\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;\"><strong>\u70b9\u4e0e\u7ebf\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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<\/div>\n<p><strong>\u91cd\u8981\u63d0\u793a\uff1a<\/strong>\u8bf7\u6ce8\u610f\uff0c\u516c\u5f0f\u4e2d\u76f4\u7ebf\u7684\u65b9\u7a0b\u662f\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b\u7684\u5f62\u5f0f\uff0c\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u6709\u4ee5\u53e6\u4e00\u79cd\u7c7b\u578b\u7684\u65b9\u7a0b\u8868\u793a\u7684\u76f4\u7ebf\uff0c\u6211\u4eec\u9700\u8981\u5148\u5c06\u5176\u4f20\u9012\u7ed9\u5176\u9690\u5f0f\u65b9\u7a0b\uff0c\u7136\u540e\u518d\u5c06\u5176\u4f20\u9012\u7ed9\u9690\u5f0f\u65b9\u7a0b\u3002\u6211\u4eec\u53ef\u4ee5\u5e94\u7528\u8fd9\u4e2a\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-distancia-entre-un-punto-y-una-recta\"><\/span>\u8ba1\u7b97\u70b9\u4e0e\u7ebf\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-106\"><\/div>\n<\/div>\n<p>\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u8ba1\u7b97\u70b9\u548c\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u627e\u5230\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c\u6cd5\u5f8b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/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-7ddc3d4b82281ca90fa991e092194056_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,-1) \\qquad \\qquad r: \\ 3x+4y-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"289\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u8ba1\u7b97\u70b9\u548c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u53ea\u9700\u5e94\u7528\u5176\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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u7528\u5b83\u7684\u503c\u66ff\u6362\u6bcf\u4e2a\u9879\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-5117783b26d70ca74c38e1c3f7c94505_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 3\\cdot 2 + 4\\cdot (-1)-5\\rvert}{\\sqrt{3^2+4^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"228\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\u6211\u4eec\u8ba1\u7b97\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-d1ab18e8e237f777d2ae0dfbc41055a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 6 -4-5\\rvert}{\\sqrt{9+16}} =\\cfrac{\\lvert -3 \\rvert}{\\sqrt{25}} = \\mathbf{\\cfrac{3}{5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"251\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distancia-entre-dos-rectas-paralelas\"><\/span>\u4e24\u6761\u5e73\u884c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb<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>\u8ba1\u7b97\u7ebf\u548c\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u5e94\u7528\u4e4b\u4e00\u662f\u627e\u5230\u5e73\u884c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002<\/p>\n<p>\u663e\u7136\uff0c\u8981\u7406\u89e3\u6211\u4eec\u4e0b\u9762\u5c06\u8981\u89e3\u91ca\u7684\u6982\u5ff5\uff0c\u60a8\u5fc5\u987b\u77e5\u9053<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u884c\u7ebf\u7684\u5b9a\u4e49\u548c\u4f8b\u5b50\/\">\u4ec0\u4e48\u662f\u5e73\u884c\u7ebf<\/a>\uff0c\u56e0\u6b64\uff0c\u5982\u679c\u60a8\u4e0d\u786e\u5207\u5730\u77e5\u9053\u5b83\u4eec\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u4f1a\u7ed9\u60a8\u7559\u4e0b\u4e00\u4e2a\u94fe\u63a5\uff0c\u6211\u4eec\u5c06\u5728\u5176\u4e2d\u8be6\u7ec6\u89e3\u91ca\u5b83\uff0c\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u793a\u4f8b\u7684\u5e73\u884c\u7ebf\u3002<\/p>\n<p><strong>\u8981\u627e\u5230\u4e24\u6761\u5e73\u884c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u53ea\u9700\u5728\u4e24\u6761\u7ebf\u4e0a\u53d6\u4e00\u70b9\u5e76\u8ba1\u7b97\u4ece\u8be5\u70b9\u5230\u53e6\u4e00\u6761\u7ebf\u7684\u8ddd\u79bb\u5373\u53ef\u3002<\/strong> <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/distance-entre-un-point-et-une-ligne-en-ligne.webp\" alt=\"\u70b9\u548c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\" class=\"wp-image-1960\" width=\"421\" height=\"358\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u786e\u5b9a\u4e24\u6761\u5e73\u884c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u8fd8\u9700\u8981\u4f7f\u7528\u7ebf\u4e0e\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4f7f\u7528\u516c\u5f0f\u65f6\u6211\u4eec\u5f97\u5230\u7684\u8ddd\u79bb\u4e3a 0 \u4e2a\u5355\u4f4d\uff0c\u5219\u610f\u5473\u7740\u8fd9\u4e9b\u7ebf\u5728\u67d0\u4e2a\u70b9\u5f7c\u6b64\u63a5\u89e6\uff0c\u56e0\u6b64\uff0c\u8fd9\u4e9b\u7ebf\u4e0d\u662f\u5e73\u884c\u7684\uff0c\u800c\u662f\u76f8\u4ea4\u3001\u91cd\u5408\u6216\u5782\u76f4\u7684\u3002\u5982\u679c\u60a8\u613f\u610f\uff0c\u60a8\u53ef\u4ee5\u5728\u6211\u4eec\u7684\u7f51\u7ad9\u4e0a\u67e5\u770b\u6b64\u7c7b\u7ebf\u8def\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n<p>\u90a3\u4e48\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u89e3\u51b3\u4e24\u6761\u5e73\u884c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u95ee\u9898\uff1a<\/p>\n<ul>\n<li>\u6c42\u4e0b\u5217\u4e24\u6761\u5e73\u884c\u7ebf\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-8be694174fbd8330f207d16a9fb4bb89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 2x-4y-6=0 \\qquad \\qquad s: \\ -x+2y+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"378\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u9700\u8981\u505a\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u5728\u4e00\u6761\u7ebf\u4e0a\uff08\u60a8\u60f3\u8981\u7684\u7ebf\uff09\u4e0a\u5f97\u5230\u4e00\u4e2a\u70b9\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u7ebf\u4e0a\u7684\u4e00\u4e2a\u70b9<\/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-23a7daa116b8874af1538c91f8d239de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a\u6b64\uff0c\u60a8\u5fc5\u987b\u4e3a\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\u8d4b\u503c\uff0c\u4f8b\u5982\u6211\u4eec\u5c06\u8fd9\u6837\u505a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d762821a7c6da83f02380639f43ef8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" 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-3b748efe6f89a8c847e2e6c2d5a78db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x+2y+4 =0 \\ \\xrightarrow{x \\ = \\ 0} \\ -0+2y+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"321\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u6e05\u9664\u53e6\u4e00\u4e2a\u53d8\u91cf\uff08<\/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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \uff09\u5f97\u51fa\u7684\u65b9\u7a0b\u53ef\u4ee5\u77e5\u9053\u6b64\u65f6\u5b83\u7684\u4ef7\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-91edb06d37339167f458f910de16d57b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" 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-9901e9a85409e4bcbfcbffdcf97cb175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{-4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"66\" 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-50b25376eef215b49997f236615b6d6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4ece\u76f4\u7ebf\u5f97\u5230\u7684\u70b9<\/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-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e1c\u65b9\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-a9176e7fde633e028a8349a5bc422e03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u5728\u4e00\u6761\u7ebf\u4e0a\u6709\u4e86\u4e00\u4e2a\u70b9\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u4ece\u8be5\u70b9\u5230\u53e6\u4e00\u6761\u7ebf\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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/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-451c7425d16dbf9c209df7a37777597b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 2\\cdot 0 + (-4)\\cdot (-2) +(-6)\\rvert}{\\sqrt{2^2+(-4)^2}}= \\cfrac{2}{\\sqrt{20}}=\\bm{0,45}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"398\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-distancia-entre-un-punto-y-una-recta\"><\/span>\u89e3\u51b3\u4e86\u70b9\u4e0e\u7ebf\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\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb<\/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-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c\u6cd5\u5f8b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" 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-15463bc0f037173b2283051b2e915dae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(4,2) \\qquad \\qquad r: \\ 5x-3y+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"275\" 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\u70b9\u548c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u53ea\u9700\u5e94\u7528\u5176\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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u7528\u5b83\u7684\u503c\u66ff\u6362\u6bcf\u4e00\u9879\u5e76\u8ba1\u7b97\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-e840997220799ac7d54b6efffc91533a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 5\\cdot 4 + (-3)\\cdot 2+6\\rvert}{\\sqrt{5^2+(-3)^2}}=\\cfrac{20}{\\sqrt{34}}= \\bm{3,43}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"344\" style=\"vertical-align: -20px;\"><\/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>\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u662f\u591a\u5c11<\/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-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c\u6cd5\u5f8b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff1f <\/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-41ed4564d284382ca1818f75faf32b27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-3,-1) \\qquad \\qquad r: \\  y=-3x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"276\" 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\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u76f4\u7ebf\u65b9\u7a0b\u662f\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u5f62\u5f0f\u3002\u76f8\u53cd\uff0c\u8981\u4f7f\u7528\u4ece\u70b9\u5230\u76f4\u7ebf\u7684\u8ddd\u79bb\u516c\u5f0f\uff0c\u8be5\u76f4\u7ebf\u5fc5\u987b\u8868\u793a\u4e3a\u9690\u5f0f\u65b9\u7a0b\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u53d8\u6362\u76f4\u7ebf\u5e76\u5c06\u5176\u4f20\u9012\u7ed9\u9690\u5f0f\u65b9\u7a0b\uff08\u53ea\u9700\u4f20\u9012\u65b9\u7a0b\u540c\u4e00\u4fa7\u7684\u6240\u6709\u9879\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-1e964a7afee927714fb86c7157d4b881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\  3x+y-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"142\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u76f4\u7ebf\u5df2\u7ecf\u6709\u4e86\u660e\u786e\u7684\u5f62\u5f0f\uff0c\u6211\u4eec\u73b0\u5728\u5c31\u53ef\u4ee5\u4f7f\u7528\u70b9\u548c\u76f4\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u6bcf\u4e00\u9879\u66ff\u6362\u4e3a\u5b83\u7684\u503c\u5e76\u8ba1\u7b97\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-5da11b73842cb053431781741f29cf97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 3\\cdot (-3) + 1\\cdot (-1)-5\\rvert}{\\sqrt{3^2+1^2}}=\\cfrac{\\lvert -9-1-5\\rvert}{\\sqrt{9+1}}=\\cfrac{15}{\\sqrt{10}}= \\bm{4,74}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"491\" style=\"vertical-align: -16px;\"><\/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>\u4e0b\u9762\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u662f\u591a\u5c11\uff1f <\/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-9ad10fd8e20d413e433851810e823172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ x+3y-4=0 \\qquad \\qquad s: \\ 2x+6y+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"364\" style=\"vertical-align: -4px;\"><\/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\u6211\u4eec\u5c06\u9a8c\u8bc1\u8fd9\u662f\u4e24\u6761\u5e73\u884c\u7ebf\u3002\u4e3a\u6b64\uff0c\u53d8\u91cf\u7684\u7cfb\u6570<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5fc5\u987b\u5f7c\u6b64\u6210\u6bd4\u4f8b\uff0c\u4f46\u4e0d\u4e0e\u72ec\u7acb\u9879\u6210\u6bd4\u4f8b\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-1a5385dff1a5c143885cac238927cea7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{3}{6}\\neq \\cfrac{-4}{6} \\ \\longrightarrow \\ \\text{Paralelas}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e9b\u7ebf\u662f\u5e73\u884c\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5e94\u7528\u8be5\u8fc7\u7a0b\u3002<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u4ece\u5176\u4e2d\u4e00\u6761\u7ebf\uff08\u60a8\u60f3\u8981\u7684\u7ebf\uff09\u4e2d\u83b7\u53d6\u4e00\u4e2a\u70b9\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u7ebf\u4e0a\u7684\u4e00\u4e2a\u70b9<\/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-23a7daa116b8874af1538c91f8d239de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a\u6b64\uff0c\u60a8\u5fc5\u987b\u4e3a\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\u8d4b\u503c\uff0c\u4f8b\u5982\u6211\u4eec\u5c06\u8fd9\u6837\u505a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d762821a7c6da83f02380639f43ef8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" 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-cfbc09666c2be26abbecc34491f0f0a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+6y+6=0 \\ \\xrightarrow{x \\ = \\ 0} \\ 2\\cdot 0+6y+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"325\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u6e05\u9664\u53e6\u4e00\u4e2a\u53d8\u91cf\uff08<\/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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> ) \u5f97\u5230\u7684\u65b9\u7a0b\u5373\u53ef\u77e5\u9053\u6b64\u65f6\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-d2147ae4d002aba7f27fda064a5f3d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6y=-6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" 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-011e4abb1bbc3ef5f362695736e2b1f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{-6}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"66\" 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-8330e0406bdbde3e65e8142fafceeee6_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\">\u8fd9\u6837\u4ece\u76f4\u7ebf\u4e0a\u5f97\u5230\u7684\u70b9<\/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-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e1c\u65b9\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-d4834bffe8509fbc113d7be09e378a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e00\u6761\u7ebf\u4e0a\u7684\u70b9\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u4ece\u8be5\u70b9\u5230\u53e6\u4e00\u6761\u7ebf\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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/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-04bdc4f7bf4e33872b9a1dae673198df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 1\\cdot 0 + 3\\cdot (-1) +(-4)\\rvert}{\\sqrt{1^2+3^2}}= \\cfrac{7}{\\sqrt{10}}=\\bm{2,21}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"371\" style=\"vertical-align: -16px;\"><\/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>\u8ba1\u7b97\u672a\u77e5\u6570\u7684\u503c<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f7f\u5f97\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c\u6cd5\u5f8b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u53735\u4e2a\u5355\u4f4d\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-4a67915da76e50711bd1ab382c252d0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2,5) \\qquad \\qquad r: \\ 12x-5y+k=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"299\" 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\">\u6211\u4eec\u5fc5\u987b\u9996\u5148\u5e94\u7528\u70b9\u548c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u7528\u5b83\u7684\u503c\u66ff\u6362\u6bcf\u4e00\u9879\u5e76\u7b80\u5316\u8868\u8fbe\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-33ba5ddeb270550eb80a95a092204c53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 12\\cdot (-2) + (-5)\\cdot 5+k\\rvert}{\\sqrt{12^2+(-5)^2}}= \\cfrac{\\lvert -24-25+k\\rvert}{\\sqrt{169}}=\\cfrac{\\lvert -49+k\\rvert}{13}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"501\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u95ee\u9898\u9648\u8ff0\u544a\u8bc9\u6211\u4eec\u70b9\u548c\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u5fc5\u987b\u7b49\u4e8e 5\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u7b49\u4e8e 5\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-c8ecc06c9ee4d5bb4f7af3e44ebf1554_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\lvert -49+k\\rvert}{13}=5\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"104\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u6c42\u89e3\u6240\u5f97\u65b9\u7a0b\u3002\u5206\u6570\u7684\u5206\u5b50\u4e2d\u5b58\u5728\u7edd\u5bf9\u503c\uff0c\u56e0\u6b64\u5fc5\u987b\u5206\u522b\u5206\u6790\u7edd\u5bf9\u503c\u4f55\u65f6\u4e3a\u6b63\u3001\u4f55\u65f6\u4e3a\u8d1f\uff1a <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-123\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07410ec6d53a5693ac56545b685f08fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{+(-49+k)}{13}=5\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"130\" 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-b7e23215c12b8cd48c8dc8f53034bd57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-49+k= 5 \\cdot 13\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"125\" 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-5c7ac0f20e76f3591e7dae560e8cb7c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-49+k= 65\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"103\" 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-25f3828a5779f9ac2703a313f3032d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k= 65+49\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" 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-29b0e2bdc51132eccc8e8e6b67301103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k= 114}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-08ddd02fb3360a9b6a7756d13b790c95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-(-49+k)}{13}=5\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"130\" 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-368c3ad800681e7d86460e6d175d676e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"49-k= 5 \\cdot 13\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"112\" 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-aea503c1a7fc95f936b2fe2c72e946a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"49-k= 65\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"90\" 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-ef8ec1c62a0a8d710f15466eefccf911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"49-65=k\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"90\" 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-4adfa64e85e20e7e2ada6dd8a42c5d55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-16=k}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"63\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6709\u4e24\u4e2a\u53ef\u80fd\u7684\u503c<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6b63\u786e\u7684\uff1a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5172bc9d68d6bfe4b17cbe2f1e40aa0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=114\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4efb\u4f55\u4e00\u4e2a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-796de6aa36adaf954bbb8584d094c3fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=-16.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"69\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u627e\u5230\u7528\u4e8e\u8ba1\u7b97\u70b9\u548c\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\u516c\u5f0f\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4e00\u4e9b\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u8ddd\u79bb\u7684\u7ec3\u4e60\uff0c\u751a\u81f3\u8be5\u64cd &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%82%b9%e4%b8%8e%e7%ba%bf%e4%b9%8b%e9%97%b4%e7%9a%84%e8%b7%9d%e7%a6%bb%e5%85%ac%e5%bc%8f%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0%e7%a4%ba%e4%be%8b\/\"> <span class=\"screen-reader-text\">\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb<\/span> \u67e5\u770b\u5168\u6587 &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-233","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/cn\/\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u793a\u4f8b\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u70b9\u4e0e\u7ebf\u4e4b\u95f4\u7684\u8ddd\u79bb - Mathority\" \/>\n<meta property=\"og:description\" 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