12.2.3 Dilations (continued)
Example 3 Art Application
The length of the perimeter of a rectangle after a dilation is determined in this application example. The size of the preimage rectangle and the scale factor are given. A scale factor of 3 will increase each linear dimension of the preimage by a factor of 3. The height of the image will be 3(8) = 24 in. The base of the image will be 3(12) = 36 in. The perimeter of the image is 120 in. Notice that the perimeter of the preimage was 40 inches, one third of the image perimeter.
Example 4 Drawing Dilations in the Coordinate Plane
The image of a triangle in the coordinate plane is drawn under a dilation in this example. The coordinates of the vertcies of the preimage, the scale factor, and the center of dilation are given. Given the center of dilation is the origin, the rule for the dilation with a scale factor of − 3 is ( x , y ) → ( − 3 x , − 3 y ). To determine the coordinates of the vertices of the image, apply the rule to each of the preimage vertices. Notice that the image is larger and, because of the negative in the scale factor, has been reflected in the x and y directions.
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