8.7 translations and rotations 2
TRANSCRIPT
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Daily Homework Quiz For use after Lesson 8.7
1. RST has vertices R(–1, 4), S(3, 4), and T(2, –3). Find the vertices of its image after the translation (x, y) → (x – 4, y + 5).
∆
2. Where have you seen a translation today?
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Daily Homework Quiz For use after Lesson 8.7
1. RST has vertices R(–1, 4), S(3, 4), and T(2, –3). Find the vertices of its image after the translation (x, y) → (x – 4, y + 5).
∆
ANSWER R'(–5, 9), S'(–1, 9), T'(–2, 2)
2. Where have you seen a translation today?
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Translations and Rotations
Section 8.7
P. 439 - 443
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Essential Questions
• What are the similarities and differences among transformations?
• How are the principles of transformational geometry used in art, architecture and fashion?
• What are the applications for transformations?
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• A rotation is a transformation that “TURNS” each point of a figure the same number of degrees around a common point. For our lessons, that point will be the origin (0,0).
Rotations may be clockwise or counterclockwise.
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• A rotation is a transformation that “TURNS” each point of a figure the same number of degrees around a common point. For our lessons, that point will be the origin (0,0).
Rotations may be clockwise or counterclockwise.
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• Rotation:– 90 degrees clockwise
• switch the coordinates around, and Y will become the opposite sign of the original point.
• (y, -x)– 90 degrees counterclockwise
• switch the coordinates around, and X will become the opposite sign.
• (-y, x)– 180 degrees
• “opposite” coordinates for both x and y.• (-x, -y)
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Try this on graph paper!
• A 90 degrees clockwise rotation will switch the coordinates around, and Y will become the opposite sign of the original point.
• Example P (6,2) P’ (2,- 6)
• Q (-3,4) Q’ ( , )
• W(4,0) W’ ( , )
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Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4). Find its image after a 90° clockwise rotation.
Switch the coordinates around, and Y will become the opposite sign of the original point.
(y, -x)
A’ (1,-1)B’ (1, -3)C’ (3, -3)D’ (4, -1)
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GUIDED PRACTICE for Example 2 and 3
Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4). Find its image after the given rotation.
2. 90 clockwise
ANSWER
A’ (1,-1)B’ (1, -3)C’ (3, -3)D’ (4, -1)
RULE: Switch the coordinates around, and Y will become the opposite sign of the original point.
(y, -x)
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Try these on graph paper
• 90 degrees counterclockwise rotation will switch the coordinates around, and X will become the opposite sign.
Example: P (5, 3) P’ (-3, 5)
• Q (-4,-2) Q’ (2, -4)
W (-7, 8) W’ ( , )
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Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4). Find its image after a 90° counterclockwise rotation.
Switch the coordinates around, and X will become the opposite sign. (-y, x)
A’ (-1,1)B’ (-1, 3)C’ (-3, 3)D’ (-4, 1)
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GUIDED PRACTICE for Example 2 and 3
Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4). Find its image after the given rotation.
3. 90 counterclockwise
ANSWER
A’ (-1,1)B’ (-1, 3)C’ (-3, 3)D’ (-4, 1)
RULE: Switch the coordinates around, and X will become the opposite sign. (-y, x)
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• 180 degree rotations will create “opposite” coordinates for both x and y.
Example: P (4, 1) P’ (-4, -1)• Q(-3, 5) Q’ (3, -5)• W (2, -7) W’ ( , )
180 degrees can be either clockwise or counterclockwise, the result is the SAME!
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GUIDED PRACTICE for Example 2 and 3
Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4). Find its image after a 180° rotation.
“opposite” coordinates for both x and y.(-x, -y)
A’ (-1,-1)B’ (-3, -1)C’ (-3, -3)D’ (-1, -4)
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GUIDED PRACTICE for Example 2 and 3
Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4). Find its image after the given rotation.
4. 180
ANSWER
A’ (-1,-1)B’ (-3, -1)C’ (-3, -3)D’ (-1, -4)
RULE: “opposite” coordinates for both x and y.(-x, -y)
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Homework
• Page 441 #1-3, 9, 11, 12