{"id":26917,"date":"2023-03-30T07:57:40","date_gmt":"2023-03-30T07:57:40","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26917"},"modified":"2024-02-05T09:12:22","modified_gmt":"2024-02-05T09:12:22","slug":"centroid-of-a-triangle-definition-properties-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle","title":{"rendered":"Centroid of a Triangle: Definition, Properties, Formula,\u00a0 Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-1835f5f4-3597-455f-9fcf-c70a767999fd\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle#0-what-is-the-centroid-of-a-triangle>What Is the Centroid of a Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle#3-properties-of-the-centroid-of-a-triangle>Properties of the Centroid of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle#7-centroid-and-orthocenter-of-a-triangle>Centroid and Orthocenter of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle#12-solved-examples-on-centroid-of-a-triangle>Solved Examples on Centroid of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle#13-practice-problems-on-centroid-of-a-triangle>Practice Problems on Centroid of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle#14-frequently-asked-questions-on-centroid-of-a-triangle>Frequently Asked Questions on Centroid of a Triangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-centroid-of-a-triangle\">What Is the Centroid of a Triangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Centroid of a triangle is the point where the three medians of a triangle meet. It\u2019s the point of intersection of three medians of a triangle.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A median of a triangle joins a vertex to the midpoint of the opposite side. Thus, it bisects the opposite side.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"285\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/median-of-a-triangle.png\" alt=\"Median of a triangle\" class=\"wp-image-33085\" title=\"Median of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/median-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/median-of-a-triangle-300x138.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the figure shown below, point G is called the centroid of the triangle ABC. It\u2019s the point at which the medians of a triangle coincide.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"333\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle.webp\" alt=\"Centroid of triangle\" class=\"wp-image-33086\" title=\"Centroid of triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-300x161.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-type-of-triangles-based-on-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_angle_pt.png\" alt=\"Identify the Type of Triangles Based on Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Type of Triangles Based on Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_18_20_gm.png\" alt=\"Identify Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangles_squares_pt.png\" alt=\"Identify Triangles and Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-types-of-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_types_of_triangles_pt.png\" alt=\"Identify Types of Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Types of Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/match-triangles-and-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_4_5_gm.png\" alt=\"Match Triangles and Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Match Triangles and Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_1_pt.png\" alt=\"Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            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});\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-the-centroid-of-a-triangle-definition\">The Centroid of a Triangle: Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The point of concurrency of three medians of a triangle is known as the centroid of a triangle.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The centroid of a triangle intersects all three medians of a triangle in the ratio 2:1.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the triangle ABC, the point G is the centroid.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-a-triangle.png\" alt=\"Centroid of a triangle\" class=\"wp-image-33087\" title=\"Centroid of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-a-triangle-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/separate-out-the-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-centroid-theorem\">Centroid Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>According to the centroid theorem,<\/strong> the centroid of the triangle is at $\\frac{2}{3}$ of the distance from the vertex to the midpoint of the opposite side.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-theorem.png\" alt=\"Centroid of triangle theorem\" class=\"wp-image-33088\" title=\"Centroid of triangle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-theorem-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the triangle ABC,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AG = \\frac{2}{3} AD$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$BG = \\frac{2}{3} BF$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$CG = \\frac{2}{3} CE$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-properties-of-the-centroid-of-a-triangle\">Properties of the Centroid of a Triangle<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The centroid is also known as the center of the object or the center of gravity.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">It is formed using the intersection of three medians of the triangle.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The centroid of a triangle always lies inside the triangle.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The centroid of a triangle divides all three medians into a 2:1 ratio.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-how-to-find-the-centroid-of-a-triangle-with-coordinates-of-vertices\">How to Find the Centroid of a Triangle with Coordinates of Vertices<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The centroid of a triangle can be found using the coordinates of the vertices of the given triangle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If the coordinates of the three vertices are known, then the coordinates of the centroid can be calculated by applying the centroid formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$G(x,y)= \\bigg(\\frac{x_1 + x_2+ x_3}{3},\\; \\frac{y_1 + y_2 + y_3}{3}\\bigg)$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-the-centroid-of-a-triangle-formula\">The Centroid of a Triangle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us consider a triangle $\\Delta ABC$ with vertices $A(x_1, y_1),\\; B(x_2, y_2)$, and $C(x_3, y_3)$ as shown in the figure below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"366\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-the-triangle-formula.png\" alt=\"Centroid of the triangle formula\" class=\"wp-image-33089\" title=\"Centroid of the triangle formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-the-triangle-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-the-triangle-formula-300x177.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula for the centroid of a triangle is:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$G(x,y)= \\bigg(\\frac{x_1+ x_2+ x_3}{3},\\; \\frac{y_1+ y_2+ y_3}{3}\\bigg)$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-centroid-of-a-right-triangle\">Centroid of a Right Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The intersection of three medians, drawn from the vertices of the right-angled triangle to the midpoint of the opposite sides, is known as the centroid of a right-angle triangle. In the above figure, point G is called the centroid of the right angle triangle ABC.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"373\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-right-angle-triangle.png\" alt=\"Centroid of right angle triangle\" class=\"wp-image-33090\" title=\"Centroid of right angle triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-right-angle-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-right-angle-triangle-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-centroid-and-orthocenter-of-a-triangle\">Centroid and Orthocenter of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The table below explains the four primary differences between a centroid and orthocenter of a triangle:<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td><strong>Centroid<\/strong><\/td><td><strong>Orthocenter<\/strong><\/td><\/tr><tr><td>It always lies within the triangle.<\/td><td>It may lie outside of the triangle.<\/td><\/tr><tr><td>The point of intersection of the medians is known as the centroid.<\/td><td>The point of intersection of the altitudes is known as the orthocenter.&nbsp;<\/td><\/tr><tr><td>It is usually denoted by the letter \u201cG.\u201d<\/td><td>It is usually denoted by the letter \u201cO.\u201d<\/td><\/tr><tr><td>The centroid of a triangle intersects all three medians into a 2:1 ratio.<\/td><td>It does not divide the altitudes into any particular ratio.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-centroid-and-incenter-of-a-triangle\">Centroid and Incenter of a Triangle<\/h2>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td><strong>Centroid<\/strong><\/td><td><strong>Incenter<\/strong><\/td><\/tr><tr><td>It always lies within the triangle.<\/td><td>It lies inside the triangle.<\/td><\/tr><tr><td>It is the point of intersection of the medians.<\/td><td>It is the point of intersection of the angle bisectors of three interior angles.<\/td><\/tr><tr><td>It is usually denoted by the letter \u201cG.\u201d<\/td><td>It is usually denoted by the letter \u201cI.\u201d<\/td><\/tr><tr><td>The centroid of a triangle intersects all three medians into a 2:1 ratio.<\/td><td>It does not divide the angle bisectors into any particular ratio.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-derivation-for-the-formula-of-a-triangle%E2%80%99s-centroid-proof\">Derivation for the Formula of a Triangle\u2019s Centroid (Proof)<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider a triangle $\\Delta ABC$ with vertices $A(x_1, y_1),\\; B(x_2, y_2)$, and $C(x_3, y_3)$ as shown in the figure below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"376\" height=\"218\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-proof.png\" alt=\"Centroid of triangle proof\" class=\"wp-image-33091\" title=\"Centroid of triangle proof\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-proof.png 376w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-proof-300x174.png 300w\" sizes=\"auto, (max-width: 376px) 100vw, 376px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us derive the formula of a triangle\u2019s centroid and prove that it is $(x,y) = \\bigg(\\frac{x_1+ x_2+ x_3}{3},\\; \\frac{y_1+ y_2+ y_3}{3}\\bigg)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since D is the midpoint of side BC of triangle ABC.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, by using the midpoint formula, we can find point D as $\\bigg(\\frac{x_2 + x_3}{2},\\; \\frac{y_2 + y_3}{ 2}\\bigg)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As we know that the centroid G divides the median into 2:1 ratio. Thus, we can calculate the coordinates of point G using the section formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The x-coordinate of the centroid G is given by,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = \\frac{\\bigg[2\\bigg(\\frac{x_2 + x_3}{2}\\bigg)+ 1\\bigg(x_1\\bigg)\\bigg]}{2 + 1} = \\frac{x_2+ x_3+ x_1}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow x = \\frac{x_1+ x_2+ x_3}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly we can find the y-coordinate of the centroid G, which is given by,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = \\frac{\\bigg[2\\bigg(\\frac{y_2 + y_3}{2}\\bigg)+1\\bigg(y1\\bigg)\\bigg]}{2 + 1} = \\frac{y_2+ y_3+ y_1}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow y = \\frac{y_1 + y_2 + y_3}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the coordinates of the centroid G is $G(x,y) = \\bigg(\\frac{x_1 + x_2 + x_ 3}{3},\\; \\frac{y_1 + y_ 2 + y_3}{3}\\bigg)$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-facts-about-centroid-of-a-triangle\">Facts about Centroid of a Triangle<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The centroid is also known as the center of the object or the center of gravity.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Usually the centroid or center of gravity of a human is about an inch below the navel or the center of the body.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The centroid of a triangle is at two-thirds length from the vertex of a triangle and at one-third from the midpoint of the opposite side.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we discussed the centroid of a triangle, its formula, derivations, the difference between orthocenter and centroid, and some facts and examples related to the centroid of a triangle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-solved-examples-on-centroid-of-a-triangle\">Solved Examples on Centroid of a Triangle<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>In the following figure, check whether the point P represents the centroid of the triangle or not.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"228\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-example.png\" alt=\"Centroid of triangle example\" class=\"wp-image-33092\" title=\"Centroid of triangle example\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the given triangle ABC, all sides of the triangle are equal. Also, lines from the vertex to opposite sides divide the sides into equal parts. Hence, we can say that lines from the vertex meeting at point B are the medians. Thus, point P is the point of intersection of medians, that is, the centroid of triangle ABC.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the coordinates of the centroid of the triangle if the vertices of a triangle are given as <\/strong>$(2, 1), (3, 2)$<strong>, and <\/strong>$(\u20132, 4)$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given, $(x_1, y_1) = (2, 1), (x_2, y_2) = (3, 2)$, and $(x_3, y_3) = (\u20132, 4)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The coordinates of the centroid are $G(x,y) = \\bigg(\\frac{x_1 + x_2 + x_3}{3}, \\frac{y_1 + y_2 + y_3}{3}\\bigg)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$G(x,y) = \\bigg(\\frac{2+3\\;-\\;2}{3},\\; \\frac{1+2+4}{3}\\bigg) = \\bigg(1, \\frac{7}{3}\\bigg)$<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>&nbsp;Find the coordinates of the centroid of the right angle triangle whose vertices are <\/strong>$(3,\\; 2), (2, \\;\u2013\\;3)$<strong>, and <\/strong>$(0,\\; 0)$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given, $(x_1, y_1) = (3, 2), (x_2, y_2) = (2, \\;\u2013\\;3)$, and $(x_3, y_3) = (0, 0)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The coordinates of the centroid are $G(x,y) = \\bigg(\\frac{x_1 + x_2 + x_3}{3},\\; \\frac{y_1 + y_2 + y_3}{3}\\bigg)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$G(x,y) = \\bigg(\\frac{3+2+0}{3},\\; \\frac{2\\;-\\;3+0}{3}\\bigg) = \\bigg(\\frac{5}{3},\\; \\frac{-1}{3}\\bigg)$<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>In the triangle given below if G is the centroid and AG = 12 inches. Find the length of the line segment GD and the length of the median.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"136\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-example-1.png\" alt=\"Centroid of triangle example\" class=\"wp-image-33093\" title=\"Centroid of triangle example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-example-1.png 311w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/centroid-of-triangle-example-1-300x131.png 300w\" sizes=\"auto, (max-width: 311px) 100vw, 311px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given, G is the centroid and $AG = 12$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As we know, the distance from the vertex to the centroid $= \\frac{2}{3} \\times$ the length of the median.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow AG = \\frac{2}{3} \\times AD$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow 12 = \\frac{2}{3} \\times AD$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow AD = \\frac{36}{2} = 18$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the length of the median $= 18$ inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also as we know, the centroid divides the median in the ratio 2:1.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow GD = \\frac{1}{2} \\times AG$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow GD = \\frac{1}{2} \\times 12 = 6$ inches.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-practice-problems-on-centroid-of-a-triangle\">Practice Problems on Centroid of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Centroid of a Triangle: Definition, Properties, Formula,\u00a0 Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The centroid of a triangle divides the median in the ratio ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1:2<\/div><div class=\"spq_answer_block\" data-value=\"1\">2:1<\/div><div class=\"spq_answer_block\" data-value=\"2\">1:3<\/div><div class=\"spq_answer_block\" data-value=\"3\">2:3<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 2:1<br\/>The centroid of a triangle divides the median in the ratio 2:1.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The centroid cuts each median into two segments. The longer segment is ______of the length of the median.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">half<\/div><div class=\"spq_answer_block\" data-value=\"1\">one-third<\/div><div class=\"spq_answer_block\" data-value=\"2\">two-third<\/div><div class=\"spq_answer_block\" data-value=\"3\">Three-fourths<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: two-third<br\/>The centroid cuts each median into two segments. The longer segment is two-thirds of the length of the median.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The formula of centroid can be derived with the help of which of the following formula?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Midpoint formula<\/div><div class=\"spq_answer_block\" data-value=\"1\">Distance formula<\/div><div class=\"spq_answer_block\" data-value=\"2\">Section formula<\/div><div class=\"spq_answer_block\" data-value=\"3\">Both (a) and (c) are correct.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Both (a) and (c) are correct.<br\/>The formula of centroid can be derived with the help of the midpoint and section formula.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Centroid of a triangle with vertices $(0, 0), (2, 1)$, and $(\u20132, 2)$ is____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">(0, 0)<\/div><div class=\"spq_answer_block\" data-value=\"1\">(0, 1)<\/div><div class=\"spq_answer_block\" data-value=\"2\">(1, 2)<\/div><div class=\"spq_answer_block\" data-value=\"3\">(2, 2)<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: (0, 1)<br\/>The coordinates of the centroid are $G(x,y) = \\bigg(\\frac{0+2-2}{3},\\; \\frac{0+1+2}{3}\\bigg) = (0,1)$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Centroid of a Triangle: Definition, Properties, Formula,\u00a0 Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Centroid of a Triangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The centroid of a triangle divides the median in the ratio ______.\",\n                    \"text\": \"The centroid of a triangle divides the median in the ratio ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The centroid of a triangle divides the median in the ratio 2:1.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1:2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The centroid of a triangle divides the median in the ratio 2:1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1:3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The centroid of a triangle divides the median in the ratio 2:1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2:3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The centroid of a triangle divides the median in the ratio 2:1.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2:1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The centroid of a triangle divides the median in the ratio 2:1.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The centroid of a triangle divides the median in the ratio 2:1.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The centroid cuts each median into two segments. 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The longer segment is two-thirds of the length of the median.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Three-fourths\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The centroid cuts each median into two segments. The longer segment is two-thirds of the length of the median.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"two-third\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The centroid cuts each median into two segments. The longer segment is two-thirds of the length of the median.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The centroid cuts each median into two segments. The longer segment is two-thirds of the length of the median.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The formula of centroid can be derived with the help of which of the following formula?\",\n                    \"text\": \"The formula of centroid can be derived with the help of which of the following formula?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The formula of centroid can be derived with the help of the midpoint and section formula.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Midpoint formula\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The formula of centroid can be derived with the help of the midpoint and section formula.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Distance formula\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The formula of centroid can be derived with the help of the midpoint and section formula.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Section formula\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The formula of centroid can be derived with the help of the midpoint and section formula.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Both (a) and (c) are correct.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The formula of centroid can be derived with the help of the midpoint and section formula.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The formula of centroid can be derived with the help of the midpoint and section formula.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Centroid of a triangle with vertices $$(0, 0), (2, 1)$$, and $$(\u20132, 2)$$ is____.\",\n                    \"text\": \"Centroid of a triangle with vertices $$(0, 0), (2, 1)$$, and $$(\u20132, 2)$$ is____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The coordinates of the centroid are $$G(x,y) = \\\\bigg(\\\\frac{0+2-2}{3},\\\\; \\\\frac{0+1+2}{3}\\\\bigg) = (0,1)$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"(0, 0)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The coordinates of the centroid are $$G(x,y) = \\\\bigg(\\\\frac{0+2-2}{3},\\\\; \\\\frac{0+1+2}{3}\\\\bigg) = (0,1)$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"(1, 2)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The coordinates of the centroid are $$G(x,y) = \\\\bigg(\\\\frac{0+2-2}{3},\\\\; \\\\frac{0+1+2}{3}\\\\bigg) = (0,1)$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"(2, 2)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The coordinates of the centroid are $$G(x,y) = \\\\bigg(\\\\frac{0+2-2}{3},\\\\; \\\\frac{0+1+2}{3}\\\\bigg) = (0,1)$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"(0, 1)\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The coordinates of the centroid are $$G(x,y) = \\\\bigg(\\\\frac{0+2-2}{3},\\\\; \\\\frac{0+1+2}{3}\\\\bigg) = (0,1)$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The coordinates of the centroid are $$G(x,y) = \\\\bigg(\\\\frac{0+2-2}{3},\\\\; \\\\frac{0+1+2}{3}\\\\bigg) = (0,1)$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-frequently-asked-questions-on-centroid-of-a-triangle\">Frequently Asked Questions on Centroid of a Triangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\"><strong>Where is the centroid formula used?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The centroid formula is used to find the coordinates of the centroid of a triangle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\"><strong>Where does the centroid of a triangle lie?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Centroid of a triangle always lies inside the triangle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\"><strong>What are the circumcenter and incenter of a triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The circumcenter is the point that is equidistant from all the vertices of the triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The incenter is the point that is equidistant from the sides of the triangle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\"><strong>What is the centroid of an equilateral triangle? Do the centroid, circumcenter, and orthocenter of an equilateral triangle coincide?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-7edf14ce-5d2f-48ac-ab27-ca51341b5ad8\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Centroid of an equilateral triangle is the point where all three medians meet. Yes, the centroid, circumcenter, and orthocenter of an equilateral triangle coincide.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Centroid of a Triangle? Centroid of a triangle is the point where the three medians of a triangle meet. It\u2019s the point of intersection of three medians of a triangle.&nbsp; A median of a triangle joins a vertex to the midpoint of the opposite side. Thus, it bisects the opposite side.&nbsp; In &#8230; <a title=\"Centroid of a Triangle: Definition, Properties, Formula,\u00a0 Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/centroid-of-a-triangle\" aria-label=\"More on Centroid of a Triangle: Definition, Properties, Formula,\u00a0 Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26917","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=26917"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26917\/revisions"}],"predecessor-version":[{"id":39900,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26917\/revisions\/39900"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}