# Examples of Dilations

Videos and solutions to help Grade 8 students learn some examples of dilations.

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Lessons for Grade 8
Common Core For Grade 8
## New York State Common Core Math Module 3, Grade 8, Lesson 3

### Lesson 3 Outcome

• 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.

### Lesson 3 Summary

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.

### NYS Math Module 3 Grade 8 Lesson 3

Classwork

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?

Example 2

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'.

Example 3

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'.

Exercise 3

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.