Question

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

Answer 1

The distance of triangle's centroid from the origin is `8.518` 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 `((5+9+8)/3,(2+6+5)/3)` or `(22/3,13/3)`

and its distance from origin is

`sqrt((22/3)^2+(13/3)^2)=sqrt(484/9+169/9)=sqrt(653/9)=1/3xx25.554=8.518`