Question

A triangle has corners at `(7 ,2 )`, `(2 ,6 )`, and `(3 ,1 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `5` 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 `(7,2)`, `(2.6)` and `(3,1)` is

`(1/3(7+2+3),1/3(2+6+1))` or `(4,3)`

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

`sqrt((4-0)^2+(3-0)^2)=sqrt(16+9)=sqrt25=5`