• Students know that dilations map circles to circles and ellipses to ellipses with the same shape.
• Students know that to shrink or magnify a dilated figure back to its original size from center 0 with scale factor r you must dilate the figure by a scale factor of 1/r.
Dilations map circles to circles and ellipses to ellipses.
If a figure is dilated by scale factor r, to bring the dilated figure back to the original size we must dilate it by a scale factor of 1/r. For example, if a scale factor is r = 4, then to bring a dilated figure back to the original size, we must dilate it by a scale factor r = 1/4.
Example 1 Dilate circle A, from center 0 at the origin by a scale factor r = 3.
Exercises 1 - 2
1. Dilate ellipse E, from center 0 at the origin of the graph, with scale factor r = 2. Use as many points as necessary to develop the dilated image of ellipse E.
2. What shape was the dilated image?
In the picture below, we have a triangle ABC, that has been dilated from center 0, by a scale factor of r = 1/3 It is noted by A'B'C'.
In the picture below we have a triangle DEF, that has been dilated from center r = 0, by a scale factor of r = 4. It is noted by D'E'F'.
Triangle ABC has been dilated from center 0 by a scale factor of r = 1/4 denoted by triangle A'B'C'. Using a ruler, verify that it would take a scale factor r = 4 of from center 0 to map triangle A'B'C' onto triangle ABC.
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