{"id":7057,"date":"2021-10-22T16:00:03","date_gmt":"2021-10-22T10:30:03","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7057"},"modified":"2021-10-25T09:43:32","modified_gmt":"2021-10-25T04:13:32","slug":"find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/","title":{"rendered":"Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1)"},"content":{"rendered":"

Solution :<\/h2>\n

We have line 12x – 5y + 9 = 0 and the point (2,1)<\/p>\n

Required distance = |\\(12*2 – 5*1 + 9\\over {\\sqrt{12^2 + (-5)^2}}\\)|<\/p>\n

= \\(|24-5+9|\\over 13\\) = \\(28\\over 13\\)<\/p>\n

\n

Similar Questions<\/h3>\n

If p is the length of the perpendicular from the origin to the line \\(x\\over a\\) + \\(y\\over b\\) = 1, then prove that \\(1\\over p^2\\) = \\(1\\over a^2\\) + \\(1\\over b^2\\)<\/a><\/p>\n

If the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k is equal to<\/a><\/p>\n

The x-coordinate of the incenter of the triangle that has the coordinates of mid-point of its sides as (0,1), (1,1) and (1,0) is<\/a><\/p>\n

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes, then<\/a><\/p>\n

If PS is the median of the triangle, with vertices of P(2,2), Q(6,-1) and R(7,3), then equation of the line passing through (1,-1) and parallel to PS is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have line 12x – 5y + 9 = 0 and the point (2,1) Required distance = |\\(12*2 – 5*1 + 9\\over {\\sqrt{12^2 + (-5)^2}}\\)| = \\(|24-5+9|\\over 13\\) = \\(28\\over 13\\) Similar Questions If p is the length of the perpendicular from the origin to the line \\(x\\over a\\) + \\(y\\over b\\) = …<\/p>\n

Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,48],"tags":[],"yoast_head":"\nFind the distance between the line 12x - 5y + 9 = 0 and the point (2,1)<\/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:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the distance between the line 12x - 5y + 9 = 0 and the point (2,1)\" \/>\n<meta property=\"og:description\" content=\"Solution : We have line 12x – 5y + 9 = 0 and the point (2,1) Required distance = |(12*2 – 5*1 + 9over {sqrt{12^2 + (-5)^2}})| = (|24-5+9|over 13) = (28over 13) Similar Questions If p is the length of the perpendicular from the origin to the line (xover a) + (yover b) = … Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T10:30:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:13:32+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1)\",\"datePublished\":\"2021-10-22T10:30:03+00:00\",\"dateModified\":\"2021-10-25T04:13:32+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\"},\"wordCount\":175,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Straight Line Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\",\"url\":\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\",\"name\":\"Find the distance between the line 12x - 5y + 9 = 0 and the point (2,1)\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-22T10:30:03+00:00\",\"dateModified\":\"2021-10-25T04:13:32+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Find the distance between the line 12x - 5y + 9 = 0 and the point (2,1)","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/","og_locale":"en_US","og_type":"article","og_title":"Find the distance between the line 12x - 5y + 9 = 0 and the point (2,1)","og_description":"Solution : We have line 12x – 5y + 9 = 0 and the point (2,1) Required distance = |(12*2 – 5*1 + 9over {sqrt{12^2 + (-5)^2}})| = (|24-5+9|over 13) = (28over 13) Similar Questions If p is the length of the perpendicular from the origin to the line (xover a) + (yover b) = … Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1) Read More »","og_url":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/","og_site_name":"Mathemerize","article_published_time":"2021-10-22T10:30:03+00:00","article_modified_time":"2021-10-25T04:13:32+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1)","datePublished":"2021-10-22T10:30:03+00:00","dateModified":"2021-10-25T04:13:32+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/"},"wordCount":175,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Straight Line Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/","url":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/","name":"Find the distance between the line 12x - 5y + 9 = 0 and the point (2,1)","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-22T10:30:03+00:00","dateModified":"2021-10-25T04:13:32+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1)"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7057"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=7057"}],"version-history":[{"count":2,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7057\/revisions"}],"predecessor-version":[{"id":7497,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7057\/revisions\/7497"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=7057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=7057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=7057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}