Question

A triangle has corners at `(1 ,5 )`, `(9 ,2 )`, and `(6 ,7 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of Centroid from origin is `7.087`

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 `((1+9+6)/3,(5+2+7)/3)` or `(16/3,14/3)`.

and its distance from origin is

`sqrt((16/3)^2+(14/3)^2)=sqrt(256/9+196/9)=sqrt(452/9)=1/3xxsqrt452=1/3xx21.26=7.087`