Geometry, dilation help

Question

A dilation from center O with scale factor r1 = 1/4 maps a point P to another point P’. Then a second dilation from O with scale factor r2 maps to P’ to P. What is the value of r2?

Answer 1

You want the action of both dilations to result to a dilation of 1 (bringing you back to the original), so r1 * r2 = 1, 1/4 * r2 = 1, r2 = 4.