{"id":6924,"date":"2021-10-22T01:37:42","date_gmt":"2021-10-21T20:07:42","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6924"},"modified":"2021-10-25T09:45:29","modified_gmt":"2021-10-25T04:15:29","slug":"the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/","title":{"rendered":"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"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Given mid-points of a triangle are (0,1), (1,1) and (1,0).<\/p>\n<p>So, by distance formula sides of the triangle are 2, 2 and \\(2\\sqrt{2}\\).<\/p>\n<p>x-coordinate of the incenter = \\(2*0 + 2\\sqrt{2}*0 + 2*2\\over {2 + 2 + 2\\sqrt{2}}\\)<\/p>\n<p>= \\(2\\over {2+\\sqrt{2}}\\)<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-distance-between-the-line-12x-5y-9-0-and-the-point-21\/\" aria-label=\"\u201cFind the distance between the line 12x \u2013 5y + 9 = 0 and the point (2,1)\u201d (Edit)\">Find the distance between the line 12x \u2013 5y + 9 = 0 and the point (2,1)<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-the-line-2x-y-k-passes-through-the-point-which-divides-the-line-segment-joining-the-points-11-and-24-in-the-ratio-32-then-k-is-equal-to\/\" aria-label=\"\u201cIf 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\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-p-is-the-length-of-the-perpendicular-from-the-origin-to-the-line-xover-a-yover-b-1-then-prove-that-1over-p2-1over-a2-1over-b2\/\" aria-label=\"\u201cIf 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\\)\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/let-a-b-c-and-d-be-non-zero-numbers-if-the-point-of-intersection-of-the-lines-4ax2ayc0-and-5bx2byd0-lies-in-the-fourth-quadrant-and-is-equidistant-from-the-two-axes-then\/\" aria-label=\"\u201cLet 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\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-ps-is-the-median-of-the-triangle-with-vertices-of-p22-q6-1-and-r73-then-equation-of-the-line-passing-through-1-1-and-parallel-to-ps-is\/\" aria-label=\"\u201cIf 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\u201d (Edit)\">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":"<p>Solution : Given mid-points of a triangle are (0,1), (1,1) and (1,0). So, by distance formula sides of the triangle are 2, 2 and \\(2\\sqrt{2}\\). x-coordinate of the incenter = \\(2*0 + 2\\sqrt{2}*0 + 2*2\\over {2 + 2 + 2\\sqrt{2}}\\) = \\(2\\over {2+\\sqrt{2}}\\) Similar Questions Find the distance between the line 12x \u2013 5y + &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\"> <span class=\"screen-reader-text\">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<\/span> Read More &raquo;<\/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":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>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<\/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\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"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\" \/>\n<meta property=\"og:description\" content=\"Solution : Given mid-points of a triangle are (0,1), (1,1) and (1,0). So, by distance formula sides of the triangle are 2, 2 and (2sqrt{2}). x-coordinate of the incenter = (2*0 + 2sqrt{2}*0 + 2*2over {2 + 2 + 2sqrt{2}}) = (2over {2+sqrt{2}}) Similar Questions Find the distance between the line 12x \u2013 5y + &hellip; 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 Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T20:07:42+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-25T04:15:29+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\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"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\",\"datePublished\":\"2021-10-21T20:07:42+00:00\",\"dateModified\":\"2021-10-25T04:15:29+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\"},\"wordCount\":183,\"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\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\",\"url\":\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\",\"name\":\"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\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-21T20:07:42+00:00\",\"dateModified\":\"2021-10-25T04:15:29+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/the-x-coordinate-of-the-incenter-of-the-triangle-that-has-the-coordinates-of-mid-point-of-its-sides-as-01-11-and-10-is\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"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\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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