Rectangle a'b'c'd' is the image of rectangle abcd after a dilation.

what is the scale factor of the dilation?

The scale factor for the dilation is 3.

Step-by-step explanation:

We are given that,

Rectangle ABCD is dilated to form the rectangle A'B'C'D'.

To find the scale factor, we will find the ratio of the lengths of the rectangle.

We see that,

A= (1,5) and B= (4,5). So, the length of side AB = 4-1 = 3

A'= (3,15) and B'= (12,15). So, the length of side A'B' = 12-3 = 9

So, the ratio of the sides AB : A'B' = 3 : 9 = 1 : 3.

Hence, we get that,

Length of side A'B' is 3 times the length of side AB.

This relation can be verified for other sides also.

Thus, the scale factor for the dilation is 3.