Question

A triangle has corners at `(9 ,3 )`, `(4 ,4 )`, and `(3 ,1 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `5.963` 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 `(9.3)`, `(4.4)` and `(3,1)` is

`(1/3(9+4+3),1/3(3+4+1))` or `(16/3,9/3)`

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

`sqrt((16/3-0)^2+(8/3-0)^2)=sqrt(256/9+64/9)`

= `1/3sqrt320=8/3xxsqrt5=8/3xx2.236=5.963`