9.5 Dilations

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# 9.5 Dilations - PowerPoint PPT Presentation

9.5 Dilations. Brett 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

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### 9.5 Dilations

Brett 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
• 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.

4

4

2

2

Example 3
• Scale Factor = 2
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.
Willis Tower
• The ratio of height to width is 6.45:1.
• The building is 1451 ft tall. What is the width?
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?

Actual Dimensions

• width 75 inches
• length 189 inches
• Model dimensions
• width 7 inches
• length 20 inches
• Does a dilation occur?
Jaguar Proportion
Assignments
• Assignments
• Worksheet Packet (50 points)
• 9.2 Graphing Packet (10 points)
• Review Worksheet (10 Points)
• Warm-ups (10 points)
• Extra Credit Opportunities
• pg523 #1 - 29
• Poster
• translation
• reflection
• rotation
• dilation