Question

A triangle has corners at `(9 ,3 )`, `(7 ,5 )`, and `(3 ,4 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of triangle's centroid from the origin is `7.49` units

Explanation:

The centroid of a triangle whose vertices are `(x_1,y_1)`, (x_2,y_2)`and (x_3,y_3)` is given by

`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

Hence centrid of given triangle is `((9+7+3)/3,(3+5+4)/3)` or `(19/3,4)`

and its distance from origin is

`sqrt((19/3)^2+4^2)=sqrt(361/9+16)=sqrt(505/9)=1/3xx22.4722=7.4907`