Polygon abcd, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image a′b′c′d′.the slope of c'd' is

C = (5,4)

D = (4,2)

Dilation with factor 8 => for the same x, y increase by a factor of 8

=> C' = (5, 8*4) = (5, 32)

=> D' = (4, 8*2) = (4, 16)

slope of C'D' = [32 - 16] / [5 -4 ] =16

You can also see that the slope of CD = [4 - 2] / [5 - 4] = 2

Then, the new slope is 8 times the old slope, this is it was multiplied by the same factor, 8. 

16