High School: Geometry
Similarity, Right Triangles, and Trigonometry G-SRT.1b
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
The next order of business is the scale factor, which is a number that compares the sizes of two similar objects. Students should know that we can find the scale factor by dividing the lengths of the corresponding sides in the similar objects or by comparing the distance from the center of dilation to each object. For instance, a scale factor of 2 means that one of the objects is twice as big as the other.
Students should know that dilations can make larger or smaller objects. If a larger object is created, we say that it's been expanded (the scale factor is greater than 1) and a smaller object results from contraction (the scale factor is less than 1).
Scale factors and dilations are used together when discussing and, in essence, defining similarity. If students aren't sure what you're asking them to do, we suggest going through it step by step with a simple shape like a triangle or quadrilateral. Then, you could even have them measure the side lengths of the two images and he distances from the center with a ruler to come up with a scale factor. Hopefully, an activity like that will tie all these concepts together.