1. What am I learning today? What will I do to show that I learned it?
Dilations
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.
Course 2

2. How does the scale factor determine what will happen to the figure?
Course 2
Dilations
QUESTION
How does the scale factor determine what will happen to the figure?

3. EXPANDS Dilations Scale Factor NO CHANGE
Course 2
Dilations
Scale 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 NO
CHANGE

4. How is scale factor determined?
Course 2
Dilations
QUESTION
How is scale factor determined?

5. The ratio of the MODEL’s dimensions to the ACTUAL object’s dimensions
Course 2
Dilations
The ratio of the MODEL’s dimensions to the ACTUAL object’s dimensions
Model or dilation
Actual or original

6. Example 1: Finding a Scale Factor
Course 2
5-9
Scale Drawings and Scale Models
Example 1: Finding a Scale Factor
Identify the scale factor.
Room
Blueprint
Length (in.)
144 18
Width (in.)
108
13.5
blueprint length
room length 18
144
Write a ratio using one of the dimensions. = 1 8 =
Simplify. 1 8
The scale factor is .

7. What is the equation that is used for all dilations?
Course 2
Dilations
QUESTION
What is the equation that is used for all dilations?

8. ______ x _________ = ______
Course 2
Dilations
Equation:
original
scale factor
dilation
______ x _________ = ______

9. Dilations d = 8 d = 1 Examples 4 2 d 2 .5 d
Course 2
Dilations
Examples 4 2 d
original x scale factor = dilation 4 ?
d = 8
SF: 2 2 .5 d
original x scale factor = dilation 2 ?
d = 1
SF: .5

10. How is the missing value in a dilation found?
Course 2
Dilations
QUESTION
How is the missing value in a dilation found?

11. Dilations To find the missing value: Use the equation. Substitute the
Course 2
Dilations
To find the missing value:
Use the equation. Substitute the
given information. Use a variable
for the unknown.
2. Solve for the variable.

12. Dilations s = 1.4 s = 5 Examples 4 s 5.6 2 s 10
Course 2
Dilations
Examples 4 s
5.6
original x scale factor = dilation 4
5.6
s = 1.4
SF: ? 2 s 10
original x scale factor = dilation 2 10
s = 5
SF: ?

13. How do I dilate an object on the coordinate plane?
Course 2
Dilations
QUESTION
How do I dilate an object on the coordinate plane?

14. Dilations Find the coordinates of the preimage.
Course 2
Dilations
To perform a dilation on the coordinate plane:
Find the coordinates of the preimage.
Multiply BOTH x and y by the scale factor.
Plot the new image.

15. Check It Out
Dilate the figure by a scale factor of 2. What are the vertices of the image? 10 8 6 C 4 2 A B 2 4 6 8 10

16. Check It Out: Continued
A’B’C’
ABC
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)
The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

17. Check It Out: Continued10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

18. Now 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.
Yes. All the coordinates have been multiplied by a scale factor of 2.
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)
A’(1.5,-1.5) B’(7.5,-1.5) C’(1.5,-7.5) D’(7.5,-7.5)
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)

19. Student Summary Spotlight

20. The scale factor for Hot
Course 2
Dilations
Insert Lesson Title Here
VOCABULARY K I M
dilation
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 Hot
Wheels®
cars is 1:64.