Unit 3, Lesson 3
Measuring Dilations
Geometry
3.1
Warm-up
Dilate triangle using center and a scale factor of 3.
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Dilate triangle using center and a scale factor of 3.
Here is a center of dilation and a triangle.
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We know that a dilation with center and positive scale factor, , takes a point along the ray to another point whose distance is times farther away from than is.
The triangle is a dilation of the triangle with center and with a scale factor of 2. So is 2 times farther away from than is, is 2 times farther away from than is, and is 2 times farther away from than is.
Because of the way dilations are defined, all of these quotients give the scale factor: .
If triangle is dilated from point with scale factor , then each vertex in is on the ray from P through the corresponding vertex of , and the distance from to each vertex in is one-third as far as the distance from to the corresponding vertex in .
The dilation of a line segment is longer or shorter according to the same ratio given by the scale factor. In other words, if segment is dilated from point with a scale factor of , then the length of segment is multiplied by to get the corresponding length of .
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Corresponding side lengths of the original figure and dilated image are all in the same proportion, and are related by the same scale factor, .