COMPOSITE TRANSFORMATIONS. DOES ORDER MATTER Use the composite transformation to plot A B C and A B C. 1a)

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1 U3 L1 HW OMPOSITE TRNSFORMTIONS DOES ORDER MTTER Use the coposite trasforatio to plot ad 1a) T 3,5 ry axis ( ) b) ry axis T 3,5 ( ) c) Did doig the trasforatios i a differet order atter? Explai why? 2a) rx axis RO,90 ( ) b) RO,90 rx axis ( ) c) Did doig the trasforatios i a differet order atter? Explai why?

2 DOULE REFLETIONS OVER PRLLEL LINES Plot each of the stages of the coposite trasforatio. 3a) 2 r 5 (Reflectio over x = -5 followed by a reflectio over x = -2) x = x = ircle the resultat trasforatio fro to '' ''? Rotatio Reflectio Traslatio What is the distace? What is the distace betwee the parallel lies? How do these two distaces relate to each other? 3b) 5 r 2 (Reflectio over x = -2 followed by a reflectio over x = -5) x = x = ircle the resultat trasforatio fro to '' ''? Rotatio Reflectio Traslatio What is the distace? What is the distace betwee the parallel lies? How do these two distaces relate to each other? ONJETURE (Take a guess) double reflectio over parallel lies sees to produce a (type of trasforatio). What is the relatioship betwee the distace betwee the parallel lies ad the total distace apped by each poit ( or )? I the two exaples above the oly thig that chaged was the order that we did the reflectios i. What ipact did the order have o the result?

3 DOES THE LOTION OF THE SHPE DETERMINE THE DIRETION IT MOVES? 4a) 2 r 4 (Reflectio over x = -4 followed by a reflectio over x = 2) x = x = ircle the resultat trasforatio fro to? Rotatio Reflectio Traslatio What is the distace? What is the distace betwee the parallel lies? How do these two distaces relate to each other? 4b) 2 r 4 (Reflectio over x = -4 followed by a reflectio over x = 2) x = x = ircle the resultat trasforatio fro to? Rotatio Reflectio Traslatio What is the distace? What is the distace betwee the parallel lies? How do these two distaces relate to each other? ONJETURE (Take a guess) Lookig back o these two exaples, did the startig locatio of the shape alter the directio of the trasforatio? What sees to be cotrollig the directio of the trasforatio?

4 5a) 5 r 1 y = y = (Reflectio over y = 1 followed by a reflectio over y = 5) ircle the resultat trasforatio fro to '' ''? Rotatio Reflectio Traslatio What is the distace? What is the distace betwee the parallel lies? How do these two distaces relate to each other? What directio did the traslatio go? UP DOWN RIGHT LEFT 5b) 1 r 5 y = y = (Reflectio over y = 5 followed by a reflectio over y = 1) ircle the resultat trasforatio fro to '' ''? Rotatio Reflectio Traslatio What is the distace? What is the distace betwee the parallel lies? How do these two distaces relate to each other? What directio did the traslatio go? UP DOWN RIGHT LEFT ONJETURE (Take a guess) I the two exaples the oly thig that chaged was the order that we did the reflectios. What ipact did the order have o the result? How ca you deterie whether it will go up or dow whe reflectig over two horizotal lies?

5 6. Deterie the traslatio distace ad directio fro the give iforatio. (Lies that appear to be either horizotal or vertical are.) a) b) c) r 3 uits 5 uits r r 7 uits d) e) f) 1 uits 12 uits 1.5 uits r r r g) h) i) 7 uits r 12 uits r 3 uits r

6 7. Suary of relatioships foud i previous exercises. a) Suarize why the order atters for two trasforatios. b) double reflectio over two parallel lies results i a. c) The distace of the traslatio is exactly the distace betwee the parallel lies. d) The directio of the traslatio depeds o. 8. oplete the followig a) reflectio over x = 4 followed by a reflectio over x = 9 results i a traslatio i the directio of UP DOWN RIGHT LEFT a total distace of. b) reflectio over x = -1 followed by a reflectio over x = -8 results i a traslatio i the directio of UP DOWN RIGHT LEFT a total distace of. c) reflectio over y = 7 followed by a reflectio over y = 3 results i a traslatio i the directio of UP DOWN RIGHT LEFT a total distace of. d) reflectio over y = 1 followed by a reflectio over y = 11 results i a traslatio i the directio of UP DOWN RIGHT LEFT a total distace of. 9. oplete the followig a) If you wated to traslate a shape to the right 10 uits, you could reflect over x = 3 ad the x =. b) If you wated to traslate a shape to the left 4 uits, you could reflect over x = 5 ad the x =. c) If you wated to traslate a shape up 6 uits, you could reflect over y = -1 ad the y =. d) If you wated to traslate a shape dow 1 uits, you could reflect over y = 8 ad the y =. e) If you wated to traslate a shape to the right 6 uits, you could reflect over x = ad the x = -4. f) If you wated to traslate a shape to the left 12 uits, you could reflect over x = ad the x = 1. g) If you wated to traslate a shape up 4 uits, you could reflect over y = ad the y = 2. h) If you wated to traslate a shape dow 7 uits, you could reflect over y = ad the y = -2.5.

7 10. Deterie the issig lie of reflectio. Draw it i ad coplete the coposite stateet. a) b) ry = ry = 4 ( ) c) ry = ry = 2 ( ) d) rx = rx = 1 ( ) rx = 2 rx = ( )