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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? 123. Today’s Agenda. Warm-up/HW Review Chapter 9 Review 9.5 Dilations Scale Factor enlargement reduction. Announcements. Today Review 9.5 Next Class - PowerPoint PPT Presentation
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