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# 8.7 translations and rotations 2

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### 8.7 translations and rotations 2

1. 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. 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. 3. Translations and Rotations Section 8.7 P. 439 - 443
4. 4. Essential Questions <ul><li>What are the similarities and differences among transformations? </li></ul><ul><li>How are the principles of transformational geometry used in art, architecture and fashion? </li></ul><ul><li>What are the applications for transformations? </li></ul>
5. 5. <ul><li>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. </li></ul>
6. 6. <ul><li>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. </li></ul>
7. 10. <ul><li>Rotation : </li></ul><ul><ul><li>90 degrees clockwise </li></ul></ul><ul><ul><ul><li>switch the coordinates around, and Y will become the opposite sign of the original point. </li></ul></ul></ul><ul><ul><ul><li>(y, -x) </li></ul></ul></ul><ul><ul><li>90 degrees counterclockwise </li></ul></ul><ul><ul><ul><li>switch the coordinates around, and X will become the opposite sign. </li></ul></ul></ul><ul><ul><ul><li>(-y, x) </li></ul></ul></ul><ul><ul><li>180 degrees </li></ul></ul><ul><ul><ul><li>“ opposite” coordinates for both x and y. </li></ul></ul></ul><ul><ul><ul><li>(-x, -y) </li></ul></ul></ul>
8. 11. Try this on graph paper! <ul><li>A 90 degrees clockwise rotation will switch the coordinates around, and Y will become the opposite sign of the original point. </li></ul><ul><li>Example P (6,2) P’ (2,- 6) </li></ul><ul><li>Q (-3,4) Q’ ( , ) </li></ul><ul><li>W(4,0) W’ ( , ) </li></ul>
9. 12. <ul><ul><li>Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after a 90° clockwise rotation. </li></ul></ul><ul><li>Switch the coordinates around, and Y will become the opposite sign of the original point. </li></ul><ul><ul><ul><li>(y, -x) </li></ul></ul></ul>A’ (1,-1) B’ (1, -3) C’ (3, -3) D’ (4, -1)
10. 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) <ul><li>RULE: Switch the coordinates around, and Y will become the opposite sign of the original point. </li></ul><ul><ul><ul><li>(y, -x) </li></ul></ul></ul>2. 90 clockwise ANSWER
11. 14. Try these on graph paper <ul><li>90 degrees counterclockwise rotation will switch the coordinates around, and X will become the opposite sign. Example: P (5, 3) P’ (-3, 5) </li></ul><ul><li>Q (-4,-2) Q’ (2, -4) </li></ul><ul><ul><li>W (-7, 8) W’ ( , ) </li></ul></ul>
12. 15. Graph A (1, 1), B (3, 1), C (3, 3), and D (1, 4) . Find its image after a 90° counterclockwise rotation. <ul><ul><ul><li>Switch the coordinates around, and X will become </li></ul></ul></ul><ul><ul><ul><li>the opposite sign. (-y, x) </li></ul></ul></ul>A’ (-1,1) B’ (-1, 3) C’ (-3, 3) D’ (-4, 1)
13. 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) <ul><ul><ul><li>RULE: Switch the coordinates around, and X will become </li></ul></ul></ul><ul><ul><ul><li>the opposite sign. (-y, x) </li></ul></ul></ul>3. 90 counterclockwise ANSWER
14. 17. <ul><li>180 degree rotations will create “opposite” coordinates for both x and y. Example: P (4, 1) P’ (-4, -1) </li></ul><ul><li>Q(-3, 5) Q’ (3, -5) </li></ul><ul><li>W (2, -7) W’ ( , ) </li></ul><ul><li>180 degrees can be either clockwise or counterclockwise, the result is the SAME! </li></ul>
15. 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. <ul><ul><ul><li>“ opposite” coordinates for both x and y. </li></ul></ul></ul><ul><ul><ul><li>(-x, -y) </li></ul></ul></ul>A’ (-1,-1) B’ (-3, -1) C’ (-3, -3) D’ (-1, -4)
16. 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) <ul><ul><ul><li>RULE: “opposite” coordinates for both x and y. </li></ul></ul></ul><ul><ul><ul><li>(-x, -y) </li></ul></ul></ul>4. 180 ANSWER
17. 20. Homework <ul><li>Page 441 #1-3, 9, 11, 12 </li></ul>