Question

A triangle has corners at `(7 ,9 )`, `(1 ,7 )`, and `(6 ,8 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of triangle's centroid from the origin is `9.262` 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 `((7+1+6)/3,(9+7+8)/3)` or `(14/3,8)`

and its distance from origin is

`sqrt((14/3)^2+8^2)=sqrt(196/9+64)=sqrt(772/9)=1/3xx27.785=9.262`