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8.7 translations and rotations 2

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  • 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)
    2. 90 clockwise ANSWER
  • 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)
    3. 90 counterclockwise ANSWER
  • 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)
    4. 180 ANSWER
  • 20. Homework
    • Page 441 #1-3, 9, 11, 12

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