8.7 translations and rotations 2
TRANSCRIPT
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).
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2. Where have you seen a translation today?
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?
Translations and Rotations
Section 8.7
P. 439 - 443
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?
• 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.
• 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.
• 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)
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’ ( , )
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)
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)
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’ ( , )
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)
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)
• 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!
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)
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)
Homework
• Page 441 #1-3, 9, 11, 12