Question

A triangle has corners at `(7 ,9 )`, `(1 ,7 )`, and `(6 ,2 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `7.6` 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 `(7,9)`, `(1.7)` and `(6,2)` is

`(1/3(7+1+6),1/3(9+7+2))` or `(14/3,18/3)`

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

`sqrt((18/3-0)^2+(14/3-0)^2)=sqrt(324/9+196/9)`

= `1/3sqrt520=1/3xx22.8=7.6`