Question

A triangle has corners at `(7 ,6 )`, `(8 ,2 )`, and `(5 ,3 )`. How far is the triangle's centroid from the origin?

Answer 1

Triangle's centroid is `7.608` 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)`, `(8.2)` and `(5,3)` is

`(1/3(7+8+5),1/3(6+2+3))` or `(20/3,11/3)`

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

`sqrt((20/3-0)^2+(11/3-0)^2)=sqrt(400/9+121/9)`

= `1/3sqrt521=1/3xx22.825=7.608`