Question

A triangle has corners at `(4 ,6 )`, `(3 ,9 )`, and `(2 ,2 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of triangle's centroid from the origin is
`6.412` 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 `((4+3+2)/3,(6+9+2)/3)` or `(3,17/3)`

and its distance from origin is

`sqrt(3^2+(17/3)^2)=sqrt(9+289/9)=sqrt(370/9)=1/3xx19.235=6.412`