Question

A triangle has corners at `(8 ,3 )`, `(4 ,-6 )`, and `(-2 ,5 )`. If the triangle is dilated by a factor of `5` about point #(1 ,-3 ), how far will its centroid move?

Answer 1

`4/3sqrt{170}`

Explanation:

The centroid of the triangle is originally at

`({8+4+(-2)}/3,{3+(-6)+5}/3)=(10/3,2/3)`

The distance of the centroid from `(1,-3)` is

`sqrt{(10/3-1)^2+(2/3-(-3))^2}=1/3sqrt{7^2+11^2}=1/3sqrt{170}`

This distance is multiplied by a factor of 5 by the dilatation. The distance the centroid will move is
`4 xx 1/3 sqrt{170} = 4/3sqrt{170}`