A triangle has corners at $(2 ,9 )$ , $(4 ,8 )$ , and $(5 ,1 )$ . How far is the triangle's centroid from the origin?

Question

1262 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-29T07:55:25

Distance of centroid from origin is $7.032$

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

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

As corners of triangle are $(2,9)$ , $(4,8)$ and $(5,1)$ , the centroid of given triangle is $((2+4+5)/3,(9+8+1)/3)$ or $(11/3,6)$ .

And its distance from origin is $sqrt((11/3-0)^2+(6-0)^2)=sqrt(121/9+36)=sqrt(121/9+324/9)$

= $sqrt((121+324)/9)=sqrt(445/9)=1/3sqrt445=1/3xx21.095=7.032$

A triangle has corners at (2 ,9 )(2 ,9 ), (4 ,8 )(4 ,8 ), and (5 ,1 )(5 ,1 ). How far is the triangle's centroid from the origin?