Question

A triangle has corners at `(9 ,1 )`, `(6 ,7 )`, and `(3 ,8 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `8.028` units away from the origin .

Explanation:

Centroid of a triangle, whose corners are `(x_1,y_1)`, `(x_2,y_2)` and `(x_3,y_3)`, is given by `(1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3))`

Hence centroid of the triangle whose corners are `(9,1)`, `(6.7)` and `(3,8)` is

`(1/3(9+6+3),1/3(1+7+8))` or `(18/3,16/3)`

And its distance from origin `(0,0)` is

`sqrt((18/3-0)^2+(16/3-0)^2)=sqrt(324/9+256/9)`

= `1/3sqrt580=1/3xx24.083=8.028`