Question

A triangle has corners at `(5 ,1 )`, `(9 ,3 )`, and `(4 ,7 )`. How far is the triangle's centroid from the origin?

Answer 1

`sqrt445/3`

Explanation:

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

`=> x_c=1/3(5+9+4)=18/3=6`

`=> y_c=1/3(1+3+7)=11/3`

Coordinates of the centroid `=(6,11/3)`

Distance `D` between the centroid and the origin :
`D=sqrt(6^2+(11/3)^2)=sqrt445/3~~7.03`