Question

A triangle has corners at `(5 ,6 )`, `(4 ,7 )`, and `(3 ,5 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `7.211` 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 `(5,6)`, `(4.7)` and `(3,5)` is

`(1/3(5+4+3),1/3(6+7+5))` or `(4,6)`

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

`sqrt((4-0)^2+(6-0)^2)=sqrt(16+36)`

= `sqrt52=7.211`