{"id":4004,"date":"2021-08-13T17:42:17","date_gmt":"2021-08-13T17:42:17","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4004"},"modified":"2021-11-30T16:31:13","modified_gmt":"2021-11-30T11:01:13","slug":"centroid-in-a-triangle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/centroid-in-a-triangle\/","title":{"rendered":"Centroid in a Triangle – Formula and Example"},"content":{"rendered":"

Here you will learn formula for centroid of triangle and how to find centroid in a triangle with example.<\/p>\n

Let’s begin –<\/p>\n

Centroid in a Triangle<\/h2>\n

If A(\\(x_1,y_1\\)), B(\\(x_2,y_2\\)) and C(\\(x_3,y_3\\)) are vertices of any triangle ABC, then<\/p>\n

The centroid is the point of the intersection of the medians(line joining the mid-point of sides and opposite vertices).<\/p>\n

Centroid divides each median in the ratio of 2 : 1.<\/p>\n

Formula for Centroid <\/h2>\n

The formula for centroid of a triangle is<\/p>\n

\n

(\\(x_1+x_2+x_3\\over 3\\),\\(y_1+y_2+y_3\\over 3\\))<\/p>\n<\/blockquote>\n

where \\(x_1\\), \\(x_2\\), and \\(x_3\\) are x-coordinates of the vertices of the triangle; and \\(y_1\\), \\(y_2\\), and \\(y_3\\) are y-coordinates of the vertices of the triangle.<\/p>\n\n\n

Example 1 : <\/span>Find the centroid of a triangle whose vertices are (6,4), (3,1) and (1,2).<\/p>\n

Solution : <\/span>Given coordinates of triangle

\n \\(x_1, y_1\\) = (5,4)

\n \\(x_2, y_2\\) = (3,3)

\n \\(x_3, y_3\\) = (1,2)

\n centroid = (\\(x_1+x_2+x_3\\over 3\\),\\(y_1+y_2+y_3\\over 3\\))

\n = (\\(5+3+1\\over 3\\), \\(4+3+2\\over 3\\))

\n = (3,3)

\n Hence centroid is (3,3)<\/p>\n\n\n\n

Example 2 : <\/span>Find the centroid of a triangle whose vertices are (0,1), (2,0) and (-3,0).<\/p>\n

Solution : <\/span>Given coordinates of triangle

\n \\(x_1, y_1\\) = (0,1)

\n \\(x_2, y_2\\) = (2,0)

\n \\(x_3, y_3\\) = (-3,0)

\n centroid = (\\(x_1+x_2+x_3\\over 3\\),\\(y_1+y_2+y_3\\over 3\\))

\n = (\\(0+2-3\\over 3\\), \\(1+0+0\\over 3\\))

\n = (\\(-1\\over 3\\), \\(1\\over 3\\))

\n Hence centroid is (\\(-1\\over 3\\), \\(1\\over 3\\))<\/p>\n\n\n

Condition for collinearity of three given points<\/h2>\n

Three given points A(\\(x_1,y_1\\)), B(\\(x_2,y_2\\)) and C(\\(x_3,y_3\\)) are collinear if any one of the following conditions are satisfied<\/p>\n

\n

(i)  Area of triangle ABC is zero.<\/p>\n

(ii)  Slope of AB = Slope of BC = Slope of AC. i.e. \\(y_2-y_1\\over {x_2-x_1}\\) = \\(y_3-y_2\\over {x_3-x_2}\\) = \\(y_3-y_1\\over {x_3-x_1}\\)<\/p>\n

(iii)  find the equation of line passing through 2 given points, if the third point satisfies the given equation of the line, then three points are collinear.<\/p>\n<\/blockquote>\n

Hope you learnt formula of centroid. To learn more practice more questions to get ahead in competition. Good Luck!<\/p>\n\n\n

\n
Next – Circumcenter of a Triangle | Incenter of Triangle<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – What is the Section Formula | Distance Formula<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn formula for centroid of triangle and how to find centroid in a triangle with example. Let’s begin – Centroid in a Triangle If A(\\(x_1,y_1\\)), B(\\(x_2,y_2\\)) and C(\\(x_3,y_3\\)) are vertices of any triangle ABC, then The centroid is the point of the intersection of the medians(line joining the mid-point of sides and …<\/p>\n

Centroid in a Triangle – Formula and Example<\/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":[32],"tags":[644,643,645],"yoast_head":"\nCentroid in a Triangle - Formula and Example - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn formula for centroid and how to find centroid in a triangle and also condition for collinearity.\" \/>\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\/centroid-in-a-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Centroid in a Triangle - 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