Question

A triangle has corners at `(1 ,4 )`, `(9 ,6 )`, and `(4 ,5 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of triangle's centroid from the origin is `6.839` 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 `((1+9+4)/3,(4+6+5)/3)` or `(14/3,5)`

and its distance from origin is

`sqrt((14/3)^2+5^2)=sqrt(196/9+25)=sqrt(421/9)=1/3xx20.518=6.839`