copyright © by holt, rinehart and winston. all rights reserved. section 8-1 dilations and scale...

Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

Section 8-1

Dilations and Scale Factors

8.1 Dilations and Scale Factors


Terms8.1 Dilations and Scale Factors

A dilation is an example of a non-rigid transformation that preserves the shape of an object and may change its size.

examples:

Notation: D(x,y) = (nx, ny)

Where the number n is called the scale factor

scale factor = Image

pre-image



1. What is the image of the point ( -1,3) transformed by the dilation D(x,y) = (4x, 4y)

What is the scale factor?


Terms8.1 Dilations and Scale Factors

In a dilation each point and its image lie on a line that passes through a point known as the center of dilation

Examples: Optics such as the iris

When the iris is relatively open it is said to be dilated


lens


2. Find the scale factor

2 cm

Center of dilation

5 cm

Pre-imageImage


definitions

If the size of a figure is reduced the dilation is called a contraction

If the size of a figure is enlarged the dilation is called an expansion

If n < 1 , the dilation is a contraction

if n > 1, the dilation is called an expansion

( n is the scale factor)



3. Find the image of the segment with endpoints (–2, 6) and (4, 2) after the dilation

D = (x, y) = 12

x, 12

y .

(–1, 3)

(2, 1)



4. Draw a dilation in a plane.

Each point on the image is 3 times as far from the center of dilation as the corresponding point on the preimage.

Dilate the triangle about A, using the scale factor 3.

preimage

A

image


assignmentPage 502 # 1-15, 18-23, 40, 41,42, and 43

copyright © by holt, rinehart and winston. all rights reserved. section 8-1 dilations and scale...

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