1. 9.5 Dilations
Brett Solberg AHS ‘11-’12

2. Warm-up Draw all the lines of symmetry. What is the angle of rotation?

3. Today’s Agenda Warm-up/HW Review Chapter 9 Review 9.5 Dilations
Scale Factor
enlargement
reduction

4. Announcements Today Next Class Homework Review 9.5 Test
Worksheet Packet
9.2 Graphing Packet
Review Worksheet

5. Transformations Translations (slide) rule of (4, -5)
Reflections (flip)
x-axis (x, y) → (x, -y)
y-axis (x, y) → (-x, y)
line

6. Rotations Center of Rotation protractor compass Rotating about Origin
90˚ clockwise (x, y) → (y, -x)
90˚ counterclockwise (x, y) → (-y, x)
180˚ either way (x, y) → (-x, -y)

7. Rotation
Rotate 90˚, 180˚, 270˚

8. Symmetry Reflection Symmetry Rotational Symmetry lines of symmetry
angle of rotation

9. Dilation
A dilation is a transformation whose image and preimage are similar.

10. Dilation
Eyes Dilating
Scale Models

11. Vocabulary
Scale Factor – determines the size change from the original figure to its image.
The dilation is an if the scale factor is greater than 1.
The dilation is a if the scale factor is between 0 and 1.
enlargement
reduction

12. Example 1
Find the scale factor. The red square is the dilation of the blue square. 4 4 2 2

13. Example 3
Scale Factor = 2

14. Example 2 Point Scale Factor Image (2, 3) 3 (6, 2) ½ (-2, 0) 2 (4, -1)
1/3
(10, 15) 20
(-10, -20)
1/5

15. Willis Tower Built in 1974, originally called the Sears tower.
Stands at 1451ft (442m)
Was the world’s tallest building for 25 years
Currently the tallest building in USA.

16. Willis Tower The ratio of height to width is 6.45:1.
The building is 1451 ft tall. What is the width?

17. Willis Tower LEGO Model (Sears Tower) scale model

18. Willis Tower Scale Model

19. Solving Proportions
The ratio of height to width is 6.45:1 If the width of the model is 3 ft, and the model is similar to the actual tower, how tall is the model?

20. Jaguar Proportion Actual Dimensions Model dimensions
width 75 inches
length 189 inches
Model dimensions
width 7 inches
length 20 inches
Does a dilation occur?

21. Assignments Assignments Extra Credit Opportunities pg 523 #1 - 29
Worksheet Packet (50 points)
9.2 Graphing Packet (10 points)
Review Worksheet (10 Points)
Warm-ups (10 points)
Extra Credit Opportunities
pg 523 #1 - 29
Poster
translation
reflection
rotation
dilation