When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation was a dilation. Generate instructions you would give another student to determine the scale factor.
Find the distance between two points on the original figure. Find the distance between the corresponding points on the transformed figure. The scale factor is the ratio of the latter distance to the former one.
_____ If you know the center of dilation is the origin, you can simply divide any non-zero coordinate of the transformed figure by the corresponding coordinate of the original figure to get the scale factor.