Question

Study the red pre-image ABDE and the associated blue dilation image A'B'D'E' below. Then select the scale factor used to create the dilation if the center of dilation is the origin.

Option A: 1/2
Option B: -1/2
Option C: 2

Option D: -2

Answer 1

Once you're told that the image is a dilation, all you need to worry about is the ratio between the lengths of sides of the original compared to lengths of sides of the image. Again, since it's a dilation, all the sides will be affected the same way, so you only need to compare one side.

Looking at the original image, side AE starts at x=1 and goes to x=4, so it's length is 3.
Looking at the dilated image, side A'E' starts at x=2 and goes to x=8, so it's length is 6.
The ratio of 6/3 = 2, so that is the scale factor.

Answer 2

The reason it's not -2 has to do with direction. Since the dilated image is further away from the center of dilation (the origin) than the original, the scale factor is positive. So, the answer is Option C.