Question

A square has vertices `J(-1,4), U(5,4), M(5,-2), P(-1, -2)`. After a dilation, square `JUMP` has vertices `J(-.5, 2), U(2.5,2), M(2.5, -1), P(-.5, -1)`. What is the scale factor of the dilation?

Answer 1

The scale factor is `=1/2=0.5`

Explanation:

Let write the coordinates as a matrix

Before dilatation `=((J,U,M,P),(-1,5,5,-1),(4,4,-2,-2))`

After dilatation `=((J',U',M',P'),(-0.5,2.5,2.5,-0.5),(2,2,-1,-1))`

We can easily see that

`0.5*((J,U,M,P),(-1,5,5,-1),(4,4,-2,-2))=((J',U',M',P'),(-0.5,2.5,2.5,-0.5),(2,2,-1,-1))`