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Envision Math 2.0: Grade 8, Volume 2

EM

Envision Math 2.0: Grade 8, Volume 2 View details

6. Describe Dilations

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Exercise 10 Page 337

A scale factor is the ratio of a length in the image to the corresponding length in the preimage.

Enlargement or reduction? Reduction
Scale factor: 13

Practice makes perfect

In the given graph, the smaller figure is the image of a dilation of the larger figure. Thecenter of dilation is the origin. We are asked to do two things.

Decide whether the dilation is an enlargement or a reduction.
Find the scale factor.

Let's do it!

Type of Dilation

There are two types of dilation.

Enlargement: The image is larger than the preimage and is produced by a scale factor greater than 1.
Reduction: The image is smaller than the preimage and is produced by a scale factor between 0 and 1.

Let's now consider the given dilation.

Image and preimage

We are told that the image is smaller than the original figure. As a result, the dilation is a reduction.

Scale Factor

The scale factor r is the ratio of a length on image to a corresponding length on the preimage. r = Length in the Image/Length in the Preimage Let's start with the preimage. In the graph we see that the width of preimage is 12 units. Its corresponding length in the image is also the width. The width of image is 4 units.

Widths

Let's substitute the values into the formula. r = Length in the Image/Length in the Preimage ⇒ r = 4/12 We can now calculate the quotient. r = 4/12 = 1/3 The scale factor for the dilation is 13.

Subchapter links

Do You Understand? p.336

Do You Know How? p.336

Practice & Problem Solving p.337-338

Assessment Practice p.338