A triangle has corners at $(7 ,9 )$ , $(1 ,7 )$ , and $(6 ,8 )$ . How far is the triangle's centroid from the origin?

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Answer 1 · 2016-05-16T08:36:46

The distance of triangle's centroid from the origin is $9.262$ units

The centroid of a triangle whose vertices are $(x_1,y_1)$ , (x_2,y_2) $and (x_3,y_3)$ is given by

$((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)$

Hence centrid of given triangle is $((7+1+6)/3,(9+7+8)/3)$ or $(14/3,8)$

and its distance from origin is

$sqrt((14/3)^2+8^2)=sqrt(196/9+64)=sqrt(772/9)=1/3xx27.785=9.262$

A triangle has corners at (7 ,9 )(7 ,9 ), (1 ,7 )(1 ,7 ), and (6 ,8 )(6 ,8 ). How far is the triangle's centroid from the origin?