Exercise 61 Page 545

Let's use the given coordinates to draw the original figure and its dilated image.

We can see that $△SQR$ and $△PMN$ have right angles, $\angle Q$ and $\angle M,$ and therefore we know that $\angle Q\cong \angle M.$ Let's use the coordinates of the vertices to find the lengths of the sides of each triangle that include the right angles.