7.2.3 Dilations and Similarity in the Coordinate Plane Key Objectives • Apply similarity properties in the coordinate plane. • Use coordinate proof to prove figures similar. Key Terms • A dilation is a transformation that changes the size of a figure but not its shape. • A scale factor describes how much the figure is enlarged or reduced. Example 1 Computer Graphics Application
A dilation of a rectangle in the coordinate plane is made in this example. The coordinates of the vertices of the rectangle and the scale factor are given. To find the image, or dilated figure, multiply the coordinates for the vertices of the preimage by the scale factor and draw the new rectangle. To multiply the coordinates, multiply each x and y value with the scale factor. Plot the points of the new figure and draw the rectangle. Because the scale factor is greater than 1, the new figure is larger than the old figure. For example, A (0, 6) is dilated to A '(0 ⋅ (4/3), 6 ⋅ (4/3)) = A '(0, 8).
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