{"id":154904,"date":"2022-03-26T00:03:09","date_gmt":"2022-03-25T18:33:09","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/orthocenter\/"},"modified":"2022-12-27T13:07:31","modified_gmt":"2022-12-27T07:37:31","slug":"orthocenter","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/orthocenter\/","title":{"rendered":"Orthocenter of a triangle formula"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/orthocenter\/#Orthocentre_of_a_Triangle_Properties\" title=\"Orthocentre of a Triangle Properties\">Orthocentre of a Triangle Properties<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/orthocenter\/#Orthocenter_Definition\" title=\"Orthocenter Definition\">Orthocenter Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/orthocenter\/#Orthocenter_Properties\" title=\"Orthocenter Properties\">Orthocenter Properties<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/orthocenter\/#How_to_Calculate_Orthocenter_of_a_Triangle\" title=\"How to Calculate Orthocenter of a Triangle :\">How to Calculate Orthocenter of a Triangle :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/orthocenter\/#1_Find_the_orthocenter_of_the_triangle_with_the_given_vertices\" title=\"1. Find the orthocenter of the triangle with the given vertices:\">1. Find the orthocenter of the triangle with the given vertices:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Orthocentre_of_a_Triangle_Properties\"><\/span>Orthocentre of a Triangle Properties<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Orthocenter of a triangle formula: A <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/orthocenter\/\">triangle<\/a> has three vertices, or corners, and three sides. The orthocentre is a special point in a triangle that is located at the intersection of the three altitudes. The altitudes are the lines that connect the vertices of a triangle to the opposite side. The orthocentre is also the centre of the triangle&#8217;s circumcircle.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154903 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/orthocenter.jpg\" alt=\"Orthocenter of a triangle formula\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/orthocenter.jpg?v=1648233186 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/orthocenter-300x212.jpg?v=1648233186 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Orthocenter_Definition\"><\/span>Orthocenter Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The orthocenter of a triangle is the intersection of its three altitudes. It is also the center of the triangle&#8217;s nine-point circle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Orthocenter_Properties\"><\/span>Orthocenter Properties<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three orthocenter properties:<\/p>\n<ol>\n<li>The orthocenter is the intersection of the three altitudes of a triangle.<\/li>\n<li>orthocenter is the center of the triangle&#8217;s nine-point circle.<\/li>\n<li>The orthocenter is also the center of the triangle&#8217;s Euler line.<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Calculate_Orthocenter_of_a_Triangle\"><\/span>How to Calculate Orthocenter of a Triangle :<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. To calculate the orthocenter of a triangle, you need to know the lengths of the three altitudes.<\/p>\n<p>Once you have the lengths of the altitudes, simply use the Pythagorean theorem to calculate the distance from each vertex to the orthocenter. The orthocenter will be the point where the three distances intersect.<\/p>\n<p>There are a few different ways to calculate the orthocenter of a triangle. The most common method is to use the coordinates of the vertices of the triangle.<\/p>\n<p>To find the orthocenter using the coordinates of the vertices, first find the equation of the line that contains the two vertices. This can be done by finding the slope of the line and then using the point-slope form of the equation of a line. Once the equation of the line is found, plug in the coordinates of the third vertex and solve for the y-coordinate. This will give you the y-coordinate of the orthocenter. To find the x-coordinate of the orthocenter, plug the y-coordinate into the equation of the line.<\/p>\n<p>Another method to find the orthocenter is to use the altitudes of the triangle. The altitude of a triangle is the perpendicular line from a vertex to the opposite side. To find the orthocenter using the altitudes, find the equations of the altitudes. These can be found by finding the slope of the altitude and then using the point-slope form of the equation of a line. Plug in the coordinates of the other two vertices and solve for the y-coordinate. This will give you the y-coordinate of the orthocenter. To find the x-coordinate of the orthocenter, plug the y-coordinate into the equation of the line.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"1_Find_the_orthocenter_of_the_triangle_with_the_given_vertices\"><\/span>1. Find the orthocenter of the triangle with the given vertices:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A(-1, 2), B(3, 4), and C(5, -6)<\/p>\n<p>The orthocenter is at the intersection of the three altitudes of the triangle. The altitudes are the lines from a vertex to the opposite side. The three altitudes are:<\/p>\n<p>AB: From A to BC<br \/>\nAC: From A to CB<br \/>\nBC: From B to CA<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Orthocentre of a Triangle Properties Orthocenter of a triangle formula: A triangle has three vertices, or corners, and three sides. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Orthocenter of a triangle formula","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn Orthocenter topic of Maths in details explained by subject experts on infinitylearn.com. 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