7.2.3 Dilations and Similarity in the Coordinate Plane (continued) Example 4 Using the SSS Similarity Theorem
The dilation of a triangle in the coordinate plane is graphed and the similarity of the two triangles is verified in this example. The coordinates of the preimage triangle are given. A scale factor of 2 is given. To determine the coordinates of the dilated triangle (image), multiply the coordinates of the preimage by the scale factor. For example, the image of A (0, 3) is A '(0·(2), 3·(2)) = A '(0, 6). Plot the points of the image and connect them with lines to draw the dilated figure. To verify that the preimage and image are similar triangles, calculate the lengths of corresponding sides using the Distance Formula. Determine the ratio of the corresponding sides in each case. The three ratios are all equal to 2. This is expected, since the scale factor used for the dilation was 2. Since the lengths of all three corresponding side pairs have a ratio of 2, △ ABC ∼ △ A ' B ' C ' by the Side-Side-Side Similarity Theorem.
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