Question

A triangle has corners at `(1 ,5 )`, `(5 ,4 )`, and `(6 ,7 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `6.667` 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 `(1,5)`, `(5.4)` and `(6,7)` is

`(1/3(1+5+6),1/3(5+4+7))` or `(4,16/3)`

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

`sqrt((4-0)^2+(16/3-0)^2)=sqrt(16+256/9)=sqrt(144/9+256/9)`

= `1/3sqrt400=1/3xx20=6.667`