What is the centroid of a triangle with corners at $(3, 1)$ $(3, 1 )$ , $(5, 2)$ $(5, 2 )$ , and $(12, 6)$ $(12 , 6 )$ ?

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What is the centroid of a triangle with corners at $(3, 1)$ $(3, 1 )$ , $(5, 2)$ $(5, 2 )$ , and $(12, 6)$ $(12 , 6 )$ ?

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Answer 1 · 2016-05-16T09:00:41

Centroid of the triangle is $(6 \frac{2}{3}, 3)$ $(6 2/3,3)$

Explanation:

The centroid of a triangle whose vertices are $(x_{1}, y_{1})$ $(x_1,y_1)$ , (x_2,y_2) $and (x_{3}, y_{3})$ $and (x_3,y_3)$ is given by

$(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$ $((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)$

Hence centroid of the triangle formed by points $(3, 1)$ $(3,1)$ , $(5, 2)$ $(5,2)$ and $12, 6)$ $12,6)$ is $(\frac{3 + 5 + 12}{3}, \frac{1 + 2 + 6}{3})$ $((3+5+12)/3,(1+2+6)/3)$ or $(\frac{20}{3}, 3)$ $(20/3,3)$ or $(6 \frac{2}{3}, 3)$ $(6 2/3,3)$

[For detailed proof for the formula see here.](http://www.learnnext.com/nganswers/ask-question/answer/How-to-derive-the-formula-of-centroid-from-section-formula/Coordinate-Geometry/84881.htm)

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What is the centroid of a triangle with corners at $(3, 1)$ $(3, 1 )$ , $(5, 2)$ $(5, 2 )$ , and $(12, 6)$ $(12 , 6 )$ ?

1 Answer

Explanation:

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What is the centroid of a triangle with corners at (3, 1 )(3,1)(3, 1 ), (5, 2 )(5,2)(5, 2 ), and (12 , 6 )(12,6)(12 , 6 )?

1 Answer

Explanation:

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What is the centroid of a triangle with corners at $(3, 1)$ $(3, 1 )$ , $(5, 2)$ $(5, 2 )$ , and $(12, 6)$ $(12 , 6 )$ ?