Before we begin, recall that a dilation is a transformation that enlarges or reduces the original figure proportionally. There are two types of dilation.
Enlargement: The image is larger than the original figure, and is produced by a scale factor greater than 1.
Reduction: The image is smaller than the original figure, and is produced by a scale factor less than 1.
We will determine the given dilation first. Then we can find the scale factor.
Dilation
Let's analyze the given dilation.
We can tell that the blue image is smaller than the black preimage. Therefore, the dilation is a reduction.
Scale Factor
The scale factor is the ratio of a length on the image to a corresponding length on the preimage. We can find the lengths of the corresponding sides of our figures in the following diagram.
Finally, we can find the scale factor.
2/6=1/3
The scale factor of our dilation is 13.
