Question

A triangle has corners at `(7 ,6 )`, `(4 ,3 )`, and `(6 ,7 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `7.782` 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 `(7,6)`, `(4,3)` and `(6,7)` is

`(1/3(7+4+6),1/3(6+3+7))` or `(17/3,16/3)`

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

`sqrt((17/3-0)^2+(16/3-0)^2)=sqrt(289/9+256/9)`

= `1/3sqrt545=1/3xx23.345=7.782`