Key Objectives • Identify and draw dilations. Key Terms • A dilation , or similarity transformation, is a transformation in which the lines connecting every point P with its image P ' all intersect at a point C , called the center of dilation , and ʹ CP CP is the same for every point P . • A dilation with a scale factor greater than 1 is an enlargement , or expansion. • A dilation with a scale factor greater than 0 but less than 1 is a reduction , or contraction. Example 1 Identifying Dilations 12.2.3 Dilations Whether a transformation is a dilation is determined in this example.
The transformation appears to be a dilation. The objects are similar and the image has not been rotated or reflected.
Whether a transformation is a dilation is determined in this example. The transformation is not a dilation. The objects are not similar, since they have the same height, and the bases are reduced in length.
Example 2 Drawing Dilations
A dilation is drawn in this example. The preimage figure is given. The center of dilation is given and the scale factor is given to be 2. To draw the dilation, draw lines from P , the center of dilation, through each of the vertices of the figure. On each of the lines, mark the point that is twice the distance from point P along that line between P and the vertex. Draw lines between the vertices of the image, A ', B ', and C ', to draw the figure.
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