Question

A triangle has corners at `(1 ,1 )`, `(8 ,2 )`, and `(5 ,9 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance `=6.2`

Explanation:

If the corners of a triangle are `(x_1,y_1), (x_2,y_2) and (x_3,y_3)`

Then, the coordinates of the centroid are

`x_c=(x_1+x_2+x_3)/3=(1+8+5)/3=14/3`

`y_c=(y_1+y_2+y_3)/3=(1+2+9)/3=12/3=4`

The distance of the centroid from the origin is

`=sqrt(x_c^2+y_c^2)=sqrt(14^2/9+16)=(sqrt340)/3=6.2`