Question

In the dilation shown above, the dark-colored figure represents the original image and the light-colored figure represents theresulting image.What is the scale factor for this dilation?

Answer 1

The scale factor k of a dilation can be found by comparing the lengths of one side of the figure before and after the dilation as follows:

$k=\frac{\text{length after the dilation}}{\text{length before the dilation}}$

Notice that the horizontal base of the original image has a length of 4 units, while the horizontal base of the image after the dilation has a length of 1 unit. Then:

$k=\frac{1}{4}$

Therefore, the scale factor for this dilation is 1/4.