Question

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

Answer 1

`sqrt458/3`

Explanation:

The coordinates of the centroid are the average of the `x` and `y` coordinates of the three vertices.

`=> x_c=1/3(1+7+5)=13/3`
`=> y_c=1/3(6+2+9)=17/3`
Coordinates of the centroid `(13/3,17/3)`

Distance between the centroid and the origin `d`:

`d=sqrt((13/3)^2+(17/3)^2)=sqrt(458/9)=sqrt458/3`