Question

A triangle has corners at `(1 ,6 )`, `(8 ,2 )`, and `(5 ,9 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `7.341` 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 `(1,6)`, `(8,2)` and `(5,9)` is

`(1/3(1+8+5),1/3(6+2+9))` or `(14/3,17/3)`

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

`sqrt((14/3-0)^2+(17/3-0)^2)=sqrt(196/9+289/9)`

= `1/3sqrt485=1/3xx22.023=7.341`