 Dilations: Scale factor

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

A dilation used to create an image larger than the original is called an enlargement.
A dilation used to create an image smaller than the original is called a reduction.

To describe a dilation we need two things: a scale factor and a center of dilation. The scale
factor tells us how the size of the “new” figure compares to the size of the old one. If the scale
factor is 1, then the two figures will be exactly the same size. If it is less than 1, the new figure
will be similar to the old one, but smaller, and if it is greater than 1, the new figure will still be
similar to the old one, but will be larger.

HOW TO FIND THE SCALE FACTOR

If you are given two shapes and need to find the scale factor, you must know which one was the original and which one is the image or the new shape.  Then you need to know the length of corresponding sides and set them up in a ratio like so: What scale factor was used to dilate rectangle WXYZ to rectangle W’X’Y’Z’? First, determine which shape is the original and which is the image.

Since the smaller one does not have the “prime” marks (the little apostrophes) it must be the original one and the one with the marks is the image.

So we set up our ratio like the one above using the lengths given. So the scale factor is 2.

The blue shape is a dilation of the black shape. What is the scale factor of the dilation?

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

 Solution: 