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: .

<p>Figure showing triangle A B C dilated to triangle A’ B’ C’ using center P and scale factor 2.</p>

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 .

<p>Figure showing triangle A B C dilated to triangle A” B” C” using center P and scale factor fraction 1 over 3.</p>

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, .

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Lesson 3

Measuring Dilations

Warm-up

Dilating Out

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Activity

All the Scale Factors

Standards Alignment

8.G.3

G-CO.2

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Activity

What Stays the Same?

Standards Alignment

G-CO.2

G-SRT.1.b

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Glossary

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Standards Alignment

8.G.3

G-CO.2

G-SRT.1

G-SRT.1.b

G-SRT.2