Question

A triangle has corners at `(3 ,5 )`, `(4 ,7 )`, and `(1 ,2 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of triangle's centroid from the origin is `5.375` 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 `((3+4+1)/3,(5+7+2)/3)` or `(8/3,14/3)`

and its distance from origin is

`sqrt((8/3)^2+(14/3)^2)=sqrt(64/9+196/9)=sqrt(260/9)=1/3xx16.125=5.375`