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# 8.7 translations and rotations 2

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### Transcript

• 1. Daily Homework Quiz For use after Lesson 8.7 2. Where have you seen a translation today? 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. Daily Homework Quiz For use after Lesson 8.7 2. Where have you seen a translation today? 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)
• 3. Translations and Rotations Section 8.7 P. 439 - 443
• 4. 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?
• 5.
• 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.
• 6.
• 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.
• 7.
• 8.
• 9.
• 10.
• 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)
• 11. 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’ ( , )
• 12.
• 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)
• 13. 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. 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)
• 14. 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’ ( , )
• 15. 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)
• 16. 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. 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)
• 17.
• 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!
• 18. 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)
• 19. 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. A’ (-1,-1) B’ (-3, -1) C’ (-3, -3) D’ (-1, -4)
• RULE: “opposite” coordinates for both x and y.
• (-x, -y)