Question

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

Answer 1

`{10 sqrt(5) }/3`

Explanation:

Centroid `C=( (1 + -3 + 7)/3 , (5 + -4 + -2)/3 ) = (5/3, -1/3)`

Dilation point: `D(-5,3)`

Distance `DC = \sqrt{ (-5 -5/3)^2 + (3 - -1/3)^2 } = {10 sqrt(5) }/3`

If we're dilating by a factor of two, we'll go from that distance away to twice that distance, moving by that distance.