Unit 7 Lesson 8.7: Dilations

CC STANDARDS

SRT 1: Verify experimentally the properties of dilations given by a center and a scale factor.

GMD 5: Know that the effect of a scale factor k greater than zero on length is to multiply by k; determine length using scale factors.

LESSON GOALS

• Define and identify a dilation as an

enlargement or a reduction.

• Use properties of dilations to solve for

variables.• Draw a dilation given

the scale factor. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

definition

IsometryA transformation that preserves lengths. Also known as a “rigid” transformation. (Figures remain congruent)

Reflections, rotations and translations are all isometries.

definition

Scale FactorThe ratio of the lengths of two corresponding sides for similar polygons

48

3032

20

48

32

3

2

30

20

3

2

Scale factor

key vocabulary

II

definition

Dilationa “nonrigid” transformation that maps a preimage onto an image that is similar.

P

P

definition

DilationReduction: the scale factor comparing the image to the preimage is between 0 and 1

I

0 1k

is the scale factork

P

I

I

P

k

I

definition

DilationEnlargement: the scale factor comparing the image to the preimage is greater than 1

P1k

is the scale factork

PI

I

P

k

example

Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement. Then, find the values of the variables.

AB

5

5

3 3

12.5

y

xz

I

definition

Describing a Dilation scale factor center of dilation

a fixed point in the plane about which all points are expanded or contracted.

P

In an enlargement, the preimage is between the center and the image.

I

definition

Describing a Dilation scale factor center of dilation

a fixed point in the plane about which all points are expanded or contracted.

P

In a reduction, the image is between the center and the preimage.

I

definitionDescribing a Dilation

Scale factor can be found by comparing corresponding side lengths Or by comparing the distance from the center to corresponding points Always compare the image to the preimage

P

PI

I

P

k

PdId

I

P

dk

d

example

A

BD

A’

B’D’

Find the scale factor. Tell whether the dilation is a reduction or an enlargement. 21.5

in

47 in21.5

47k

215

470

43

94

C

example

Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Then find the values of the variables.

example

53

Center: 0,0

k x

y

53

3,3 ' 5,5A A

A’

53

3,0 ' 5,0B B

B’

53

0, 6 ' 0, 10C C

A

B

C

C’

Draw a dilation of the figure using the given scale factor.

example

12

Center: 0,0

k

x

y

12

1 12 21,5 ' , 2D D

D’

12

4,4 ' 2,2E E

E’

12

125,2 ' 2 ,1F F

F’

12

122,3 ' 1,1G G

DE

FG

G’

1

1

2

2

summaryWhat determines if a dilation is an enlargement or

a reduction?

How do you find the scale factor of a dilation?

A friend asks you with help on the following problem; Draw the dilation of the figure using the given scale factor.

Explain to your friend how they should solve this problem.

Today’s Assignment

worksheet