Question

A triangle has corners at `(3 ,1 )`, `(1 ,-2 )`, and `(-4 ,-5 )`. If the triangle is dilated by a factor of `5` about point #(7 ,-6 ), how far will its centroid move?

Answer 1

`4 sqrt{65}`

Explanation:

The centroid is the center of mass of the triangle and is given by the average of the coordinates:

`C=\frac 1 3(3+1-4,1-2-5)=(0,-2)`

The distance from the centroid to the dilation point `(7,-6)` is

`d = \sqrt{(0-7)^2+(-2 - -6)^2} = sqrt{65}`

The factor of five dilation means this will end up `5 sqrt{65}` from the dilation point after dilation, so will have moved `4 sqrt{65}`.