Question

A triangle has corners at `(5 ,4 )`, `(9 ,3 )`, and `(2 ,7 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance is `sqrt452/3`

Explanation:

The centroid of the triangle is `((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

So the centroid is `((5+9+2)/3,(4+3+7)/3)=(16/3,14/3)`
Let the centroid be `(x_c,y_c)`
The distance of the centroid from the origin is `sqrt(x_c^2+y_c^2)`

`=sqrt(16^2+14^2)/3=sqrt452/3`