In the table below, write the coordinates of each point in the figure. Point x-coordinate y-coordinate A 0 3 B 3 3 C 3 5 D 3 8 E 5 5 F 6 3 G 3 1

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Alfred Phillips
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1 1 TASK 1.1.1: PATTY PAPER TRANSFORMATIONS Solutions 10 D C E A B F G In th tabl blow, writ th s of ach pot th figur. x- y- A 0 3 B 3 3 C 3 5 D 3 E 5 5 F 3 G On patty papr, trac th figur from th prvious graph (clud th axs for rfrnc). Usg th patty papr, do ach of th transformations listd a-f on th origal figur. Aftr ach transformation, rcord ( th tabl providd) th s of th imags of th labld pots from th primag. Dscrib and symbols any pattrns you s. a. Translat th primag down units b. Translat th primag to th lft 3 units. x- y- A 0 1 B 3 1 C 3 3 D 3 E 5 3 F 1 G 3-1 Sam valus Dcrasd by x y - x- y- A -3 3 B 0 3 C 0 5 D 0 E 5 F 3 3 G 0 1 Dcrasd Sam valus by 3 x- 3 y Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

2 c. Translat th primag right 1 unit and up units x- y- A 1 5 B 5 C 7 D 10 E 7 F 7 5 G 3 Symbol s Incrass by 1 Incrass by x+1 y+ d. Translat th primag lft units and down 1 unit. x- y- A - B -1 C -1 D -1 7 E 1 F G -1 0 Symbol s Dcrass by Dcrass by 1 x- y-1. Rflct th primag about th x-axis. x- y- A 0-3 B 3-3 C 3-5 D 3 - E 5-5 F -3 G 3-1 Symbol s No chang Opposit signs x -y f. Rflct th primag about th y-axis. x- y- A 0 3 B -3 3 C -3 5 D -3 E -5 5 F - 3 G -3 1 Opposit signs Symbol s No chang -x y Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

3 3. In gomtry, ach of th transformations can b gnralizd by usg notation.for xampl, whn th primag pot (, ) is translatd to th lft and up to produc th imag pot (, ), th corrspondg notation would b # & T :( x,y)! x ", y + $ % ' (.Usg th formation from th tabls part 1 and notation, complt th tabl blow. Transformation Gnralization a. Translatd down units th x-s stayd th sam y s dcrasd by! y b. Translatd lft 3 units- x-s dcrasd by! x and th y s ar th sam c. Translatd right 1 and up th x s crasd by 1! x + 1 and y s crasd by! y + d. Translatd lft and down 1- x s dcrasd by! x and y s dcrasd by 1! y 1. Rflctd ovr th x-axis- x s stayd th sam th y-s wr th opposit signs. f. Rflctd ovr th y-axis- x s had th opposit signs and y stayd th sam. ( )! ( x, y " ) T : x, y T :( x, y)! ( x ", y) T :( x, y)! ( x + 1, y + ) T :( x, y)! ( x ", y " 1) R :( x, y)! ( x," y) R :( x, y)! ("x, y) 3. Th graph blow shows both th origal primag and its imag undr a transformation. Dscrib th transformation and usg notation. 10 D D' C E A B F C' G' G A' B' G' - - Th imag is translatd 5 to th lft and 3 down. Usg notation, T : x, y ( )! ( x " 5, y " 3) Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

4 Math nots Transformations ar taught both gomtry and algbra, but th contxt and th notation is diffrnt. Algbra II tachrs who hav not taught gomtry may b unfamiliar with th notation and pdagogical approach for tachg studnts to writ transformations gomtry. Howvr, as th Algbra II studnts ar askd to writ transformations usg function notation, it is important for Algbra II tachrs to undrstand th prior mathmatical xposur that may b causg som studnt misundrstandgs about transformations. Tachg nots It is vry important that tachrs xprc usg th patty papr to do th translations that ar this task. Patty papr is a common tool usd whn xplorg transformations gomtry. ** Not: Patty papr is squar, lightly waxd papr that is usd as a manipulativ for dog constructions and othr xplorations gomtry classrooms. It is actually th papr that is usd to sparat hamburgr pattis and can b purchasd at most rstaurant supplirs. Th structor may want to modl th tracg of th figur on th ovrhad. (You can us a squar pic of transparncy film to modl for participants.) Whn tracg th figur participants nd to also copy th x- and y- axs to assist aligng thir copy whn thy do th transformations dscribd Exrcis 1. As a class (so that studnts undrstand how to us th patty papr and th mannr which thy nd to rcord thir obsrvations of what happns aftr ach transformation), work through Exrcis 1a. Aftr Exrcis 1a is modld, hav participants work pairs to complt th othr tabls. Aftr participants hav compltd th tabls Exrcis 1, hav thm compar thir answrs with anothr pair. For Exrcis, complt th first ntry th tabl as a class. Undr th transformation column participants ar xpctd to giv a writtn dscription of th translation and its rprsntation notation th gnralization column. Hav rprsntativs from th groups prsnt thir fdgs to th class. Exrcis 3 is cludd as a brif assssmnt to s if participants hav graspd th us of notation to dscrib transformations. Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

5 5 TASK PATTY PAPER TRANSFORMATIONS 10 D C E A B F G In th tabl blow, writ th s of ach pot th figur. x- y- Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

6 1. On patty papr, trac th figur from th prvious graph (clud th axs for rfrnc). Usg th patty papr, do ach of th transformations listd a-f on th origal figur. Aftr ach transformation, rcord ( th tabl providd) th s of th imags of th labld pots from th primag. Dscrib and symbols any pattrns you s. a. Translat th primag down units. x- y- c. Translat th primag right 1 unit and up units. x- y- b. Translat th primag to th lft 3 units. x- y- d. Translat th primag lft units and down 1 unit. x- y- Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

7 7. Rflct th primag about th x-axis. f. Rflct th primag about th y-axis. x- y- x- y- Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

8 . In gomtry, ach of th transformations can b gnralizd by usg notation. For xampl, whn th primag pot (, ) is translatd to th lft and up to produc th imag # & pot (, ), th corrspondg notation would b T :( x, y)! x ", y + $ % ' (. Usg th formation from th tabls part 1 and notation, complt th tabl blow. Transformation ( Dscriptions from tabls) Gnralization (Usg notation) a. b. c. d.. f. Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

9 9 3. Th graph blow shows both th primag and its imag undr a transformation. Dscrib th transformation both and usg notation. 10 D D' C E A B F C' G' G A' B' G' - - Dcmbr 10, 00. Ensurg Tachr Quality: Algbra II, producd by th Charls A. Dana Cntr at Th Univrsity of Txas at Aust for th Txas Highr Education Coordatg Board.

Alpha and beta decay equation practice

Alpha and beta decay equation practice Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit