9.5 dilations

9.5 DILATIONSBrett Solberg AHS ‘11-’12

Warm-up• Draw all the lines of symmetry. What is the angle of

rotation?

• 1 2 3

Today’s Agenda• Warm-up/HW Review

• Chapter 9 Review

• 9.5 Dilations• Scale Factor

• enlargement • reduction

Announcements• Today

• Review• 9.5

• Next Class• Test

• Homework • Worksheet Packet• 9.2 Graphing Packet• Review Worksheet

Transformations

• Translations (slide)• rule of (4, -5)

• Reflections (flip)• x-axis (x, y) → (x, -y)• y-axis (x, y) → (-x, y)• line

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)

Rotation

• Rotate 90˚, 180˚, 270˚

Symmetry• Reflection Symmetry

• lines of symmetry

• Rotational Symmetry• angle of rotation

Dilation• A dilation is a transformation whose image and preimage

are similar.

Dilation• Eyes Dilating

• Scale Models

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

Example 1• Find the scale factor. The red square is the dilation of the

blue square.

2

2

4

4

Example 3• Scale Factor = 2

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

• 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.

Willis Tower

• The ratio of height to width is 6.45:1.

• The building is 1451 ft tall. What is the width?

Willis Tower

Willis Tower LEGO Model (Sears Tower)

scale model

Willis Tower Scale Model

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?

Solving Proportions

Jaguar Proportion• Actual Dimensions

• width 75 inches• length 189 inches

• Model dimensions• width 7 inches• length 20 inches

• Does a dilation occur?

Assignments• Assignments

• 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