Question

A triangle has corners at `(1 ,5 )`, `(3 ,-9 )`, and `(-1 ,-4 )`. If the triangle is dilated by a factor of `5` about point #(-1 ,-2 ), how far will its centroid move?

Answer 1

Distance moved by centroid `vec(GG') ~~ 8.11`

Explanation:

Dilation factor 5, dilated about D (-1,-2)

Centroid `G = (1+3-1)/3, (5-9-4)/3 => ((1),(-8/3))`

`bar(G'D) = 5 * bar(GD)`

`G'((x+1),(y+2)) = 5 * ((1+1),(-8/3+2)) => ((10),(-10/3))`

`G'((9),(-4/3))`

`vec(G'G) = sqrt((9-1)^2 + (-4/3 + 8/3)^2) ~~ 8.11`