A triangle has corners at $(7 ,2 )$ , $(6 ,7 )$ , and $(3 ,5 )$ . How far is the triangle's centroid from the origin?

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Answer 1 · 2018-04-25T15:19:35

The centriod is the average of the coordinates:

$C=( {7+6+3}/3, {2+7+5}/3) = (16/3, 14/3)$

so its distance to the origin is

$\sqrt{(16/3)^2 + (14/3)^2}=sqrt{ (2/3)^2(8^2+7^2) } = 2/3 sqrt{113}$

A triangle has corners at (7 ,2 )(7 ,2 ), (6 ,7 )(6 ,7 ), and (3 ,5 )(3 ,5 ). How far is the triangle's centroid from the origin?