Question

A triangle has corners at `(3 ,4 )`, `(9 ,3 )`, and `(2 ,7 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `6.6` 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 `(3,4)`, `(9.3)` and `(2,7)` is

`(1/3(3+9+2),1/3(4+3+7))` or `(14/3,14/3)`

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

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

= `1/3sqrt392=1/3xx19.8=6.6`