Course 2

What am I learning today?Dilations

What will I do to show that I learned it?

Given a figure in the coordinate plane, determine the coordinates

resulting from a dilation.

Dilations

Course 2

Dilations

QUESTIONHow does the scale

factor determine what will happen to the

figure?

Course 2

DilationsScale Factor

If your scale factor is greater than 1,

the image

If your scale factor is less than 1, the

image

If your scale factor is 1, there is

EXPANDS

SHRINKS

CHANGENO

Course 2

Dilations

QUESTIONHow is scale factor

determined?

Course 2

Dilations

The ratio of the MODEL’s dimensions to the ACTUAL

object’s dimensions

Model or dilation

Actual or original

Identify the scale factor.

Example 1: Finding a Scale Factor

Course 2

5-9 Scale Drawings and Scale Models

Room Blueprint

Length (in.) 144 18

Width (in.) 108 13.5

blueprint lengthroom length

= 18

18

The scale factor is .

Write a ratio using one of the dimensions.

Simplify.

18144

=

Course 2

Dilations

QUESTIONWhat is the equation

that is used for all dilations?

Course 2

Dilations

Equation:

______ x _________ = ______original scale factor dilation

Course 2

DilationsExamples

2 ?

original x scale factor = dilation2 .5 d

4 ?

original x scale factor = dilation4 2

SF: 2

d

SF: .5

d = 8

d = 1

Course 2

Dilations

QUESTIONHow is the missing value in a dilation

found?

Course 2

Dilations

1. Use the equation. Substitute the given information. Use a variable for the unknown.

2. Solve for the variable.

To find the missing value:

Course 2

DilationsExamples

2 10

original x scale factor = dilation2 s 10

4 5.6

original x scale factor = dilation4 s

SF: ?

5.6

SF: ?

s = 1.4

s = 5

Course 2

Dilations

QUESTIONHow do I dilate an

object on the coordinate plane?

Course 2

Dilations

1. Find the coordinates of the preimage.

2.Multiply BOTH x and y by the scale factor.

3.Plot the new image.

To perform a dilation on the coordinate plane:

Course 3

5-6 Dilations

Check It Out

Dilate the figure by a scale factor of 2. What are the vertices of the image?

2

4

2 4 6 8 100

6

8

10

B

C

A

Course 3

5-6 Dilations

Check It Out: Continued

A(2, 2) A’(2 2, 2 2) A’(4, 4)

B(4, 2) B’(4 2, 2 2) B’(8, 4)

C(2, 4) C’(2 2, 4 2) C’(4, 8)

ABC A’B’C’

The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

Course 3

5-6 Dilations

Check It Out: Continued

2

4

2 4 6 8 100

6

8

10

B’

C’

A’

B

C

A

Course 3

5-6 DilationsNow Try These…

1. Tell whether the transformation is a true dilation. A(0, 4) B(5,5) C(3,3) A’(0, 8) B’(10, 10) C’(6, 6) Explain.

2. Dilate the figure by a scale factor of 1.5. What are the coordinates of the dilated image? A(1,-1) B(5,-1) C(1,-5) D(5,-5)

3. Dilate the figure by a scale factor of 2. What are the coordinates of the image? A(2,4) B(5,6) C(6,1)

A’(4,8) B’(10,12) C’(12,2)

Yes. All the coordinates have been multiplied by a scale factor of 2.

A’(1.5,-1.5) B’(7.5,-1.5) C’(1.5,-7.5) D’(7.5,-7.5)

Student Summary Student Summary SpotlightSpotlight

19

Insert Lesson Title Here

Course 2

DilationsVOCABULARY

KK II MMdilation - transformation

- causes figure to increase or decrease proportionately

Eye doctors “dilate” your eyes

scale factor

- ratio- enlarges or shrinks similar figures The scale factor for HotThe scale factor for Hot

Wheels®Wheels®cars is 1:64.cars is 1:64.