G.CO.A.5 WORKSHEET #9 geometrycommoncore NAME: 1 DOUBLE REFLECTIONS OVER INTERSECTING LINES Plot each of the stages of the composite transformation.
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1 G.CO.A.5 WORKSHT #9 geoetrycoocore NAM: 1 OUBL RLCTIONS OVR INTRSCTING LINS Plot eac of te stages of te coposite trasforatio. 1a) r r ( ABC) Circle te resultat trasforatio fro ABC to A B C? Rotatio Reflectio Traslatio How did you recogize wic trasforatio apped A to A, B to B ad C to C? C (3,-4) B (5,-7) A (6,-1) Wat is te agle betwee te itersectig lies of reflectio (te x & )? _ Wat is te AOA? Wat is te relatiosip betwee AOA ad te agle betwee te itersectig lies of reflectio? 1b) r r ( ABC) Circle te resultat trasforatio fro ABC to A B C? Rotatio Reflectio Traslatio How did you recogize wic trasforatio apped A to A, B to B ad C to C? C (-6,0) B (-7,-4) A (-2,-2) Wat is te agle betwee te itersectig lies of reflectio (te x & )? _ Wat is te AOA? Wat is te relatiosip betwee AOA ad te agle betwee te itersectig lies of reflectio? CONJCTUR (Tae a guess) A double reflectio over itersectig lies sees to produce a (type of trasforatio). Wat is te relatiosip betwee te agle betwee te itersectig lies of reflectio ad te agle tat eac poit oves (AOA or BOB or COC )
2 G.CO.A.5 WORKSHT #9 geoetrycoocore 2 OS TH ORR MATTR? y = x lie 2a) r r ( ABC) y x A (7,-4) B (3,-2) C (6,-1) Reflect over te r ( x, y) x, y B (3,-2) C (6,-1) A (7,-4) Reflect over te y = x lie r x y y x y x A (, B (, C (, eterie te geeral resultat coordiate rule for tis double reflectio over itersectig lies? P( x, y) P''(, Tis rule sould be failiar wat is it te rule B (3,-2) y = x lie C (6,-1) A (7,-4) 2b) r r ( ABC) y x A (7,-4) B (3,-2) C (6,-1) Reflect over te y = x lie r x y y x y x A (, B (, C (, Reflect over te r ( x, y) x, y eterie te geeral resultat coordiate rule be for tis double reflectio over itersectig lies? P( x, y) P''(, Tis rule sould be failiar wat is it te rule How did te order ipact te results of tese two exaples? Te acute betwee tese te two itersectig lies ( & y = x lie) of reflectio is 45. I 2a, te resultat rotatio was 90 ad i 2b, te resultat rotatio was -90. Mae a coecture about tis relatiosip.
3 G.CO.A.5 WORKSHT #9 geoetrycoocore 3 I a earlier obective (G.CO.4) we discussed ow rotatios of a give aout ave a ifiite aout of co-terial agles; for exaple 90 = ). We worig wit te agle betwee te two itersectig lies of reflectio it is a covetio to use te acute agle value ad ot its obtuse suppleet C (-2,2) A (1,6) B (2,4) y = x lie 3a) r r ( ABC) y x A (1,6) B (2,4) C (-2,2) Reflect over te r ( x, y) x, y Reflect over te y = x lie r x y y x y x A (, B (, C (, eterie te geeral resultat coordiate rule for tis double reflectio over itersectig lies? P( x, y) P''(, Tis rule sould be failiar wat is it te rule C (-2,2) A (1,6) B (2,4) y = x lie 3b) r r ( ABC) y x A (1,6) B (2,4) C (-2,2) Reflect over te y = x lie r x y y x y x A (, B (, C (, Reflect over te r ( x, y) x, y eterie te geeral resultat coordiate rule be for tis double reflectio over itersectig lies? P( x, y) P''(, Tis rule sould be failiar wat is it te rule How ca you deterie te size ad directio (positive or egative) of te resultat rotatio?
4 G.CO.A.5 WORKSHT #9 geoetrycoocore 4 4. eterie te resultat rotatio agle value fro te double reflectio over itersectig lies. (More ta oe aswer is possible for eac of tese questio we will use acute agle to deterie te rotatio value.) a) b) c) 38 r 54 r 72 r Resultat Rotatio Agle Value Resultat Rotatio Agle Value Resultat Rotatio Agle Value d) e) f) 19 r 86 r 70 r Resultat Rotatio Agle Value Resultat Rotatio Agle Value Resultat Rotatio Agle Value 5. Suary of relatiosips foud i previous exercises. a) A double reflectio over two itersectig lies results i a (type of trasforatio). b) Te agle of rotatio of te double reflectio over itersectig lies is exactly te agle betwee te itersectig lies. c) Te directio of te rotatio depeds o _.
5 G.CO.A.5 WORKSHT #9 geoetrycoocore 5 6. Coplete te followig a) If you wated to rotate a sape by 90 by double reflectig it over two itersectig lies, te agle betwee te two itersectig lies would eed to be. b) If you wated to rotate a sape by 110 by double reflectig it over two itersectig lies, te agle betwee te two itersectig lies would eed to be. c) If you wated to rotate a sape by 24 by double reflectig it over two itersectig lies, te agle betwee te two itersectig lies would eed to be. d) If you wated to rotate a sape by 200 by double reflectig it over two itersectig lies, te agle betwee te two itersectig lies would eed to be. 7. eterie te followig for ay poit P. a) Usig te 30 agle as te agle of itersectio, would r r ( P) be a positive or egative rotatio? b) Usig te 83 agle as te agle of itersectio, would r r ( P) be a positive or egative rotatio? c) Usig te 30 agle as te agle of itersectio, would r r ( P) be a positive or egative rotatio? 8. eterie te followig for ay poit P. a) r P would result i a rotatio of -60. b) r P would result i a rotatio of 134. c) r P would result i a rotatio of d) r P would result i a rotatio of eterie te followig for ay poit P. a) r r ( P) would result i a rotatio of _. b) r r ( P) would result i a rotatio of _ c) r r ( P) would result i a rotatio of _. 37 g d) r r ( P) would result i a rotatio of _. g e) r r ( P) would result i a rotatio of _. g 75
6 G.CO.A.5 WORKSHT #9 geoetrycoocore If te order tat we do tese reflectios atters as to weter te rotatio is positive or egative, wy does t it atter for tese two coposite trasforatios, r r ( ABC) ad r r ( ABC) 11. Coplete te coposite trasforatio so tat it correct. B C 21 B C 21 A A O O r r ( ABC) RO,42( ABC) r r ( ABC) RO, 42( ABC) 12. Te followig questio was foud i te oewor ad two studets aswered it differetly. r Studet #1 Studet # Wat is te rotatio agle? Aswer: -148 Aswer: +212 Wy are bot of tese aswers correct?
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