Dilations & Similar Figures

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center point and a scale factor.

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

AB = 2.

The scale factor is 3.

Two figures are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

To find the scale factor, divide the length of a side of the image by the length of the corresponding side of the original figure.

The scale factor 8 would create a larger image.

The ratios of the lengths of corresponding sides of similar figures are equal to the scale factor.

If the scale factor is 2, the area of the figure increases by a factor of 2^2 = 4.

If the scale factor is k, then the ratio of the areas of two similar figures is k^2.