ࡱ> BDA3  bjbj΃ ilddddddd$p4444333       $ 1d3@3331dd44F3 d4d4 3 ndd4 `X=\0@ @ x ddddNotes Transformations: Rotations Lets take a look at some real life application of rotations:  HYPERLINK "http://www.regentsprep.org/Regents/math/geometry/GT4/Lrotate.htm" http://www.regentsprep.org/Regents/math/geometry/GT4/Lrotate.htm A _________ is a transformation that turns a figure about a fixed point called the __________________. Rays drawn from the center of rotation to a point and its image form an angle called the _______________. An object and its rotation are the _______________________, but the figures may be _____________________ __________________________________. Rotations are ______________!Some practices of what rotations look like:  HYPERLINK "http://www.regentsprep.org/Regents/math/geometry/GT4/PracRot.htm" http://www.regentsprep.org/Regents/math/geometry/GT4/PracRot.htm A (2,3) B (3,-2) C (2,1) 90 Clockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A(2,3) B (3,-2) C (-2,1) 90 Counterclockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A (2,3) B (3,-2) C (-2,1)  180 Clockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A (2,3) B (3,-2) C (-2,1)  180 Counterclockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A (2,3) B (3,-2) C (-2,1)  270 Clockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A (2,3) B (3,-2) C (-2,1)  270 Counterclockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A(2,3) B (3,-2) C (-2,1)  360 Clockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A (2,3) B (3,-2) C (-2,1)  360 Counterclockwise Coordinates of Pre- Image Coordinates of the Image (after Rotation) A(2,3) B (3,-2) C (-2,1) See if you could come up with the rules for rotation! Degrees of RotationClockwise RuleCounterclockwise Rule90  180  270  360   Ex. 1) Draw the rotation of  EMBED Equation.3  under a rotation of 90 counterclockwise about the origin. Give the coordinates of  EMBED Equation.3 . Ex. 2) Draw the rotation of  EMBED Equation.3  under a rotation of 180 about the origin.  Give the coordinates of  EMBED Equation.3 . bcI[ UVuvwy6ɺۇyny`nW0JOJQJ^JjOJQJU^JjOJQJU^JOJPJQJ^J jU OJQJ^JCJOJQJ^JaJ#5B*CJOJQJ\^JaJphB*CJOJQJ^JaJphB*CJOJQJ^JaJ0ph#5B*CJOJQJ\^JaJ0phCJOJQJ^JCJOJQJ^JaJ00JjU jU""#2Xvxy89U}}}}[$\$k$$Ifl0\(dd064 la$If$If  67 )*45?@AB    & ' 1 2 3 4     " # $ % x y      j_aN CJUVaJ jUOJPJQJ^JjOJQJU^JVUb|v$v,v,vl$K$L$Ifl0,g 064 la$IfK$[$\$ $If[$\$  ()*345>?v(v,v,l$K$L$Ifl0,g 064 la$IfK$[$\$ $If[$\$ ?@A $If[$\$l$K$L$Ifl0,g 064 laABCQkxx$IfK$[$\$ $If[$\$k$$Ifl0\(dd064 la(,,vvv $If[$\$$IfK$[$\$l$K$L$Ifl0,g 064 la      % & ' 0 1 2 3 (,,v $If[$\$l$K$L$Ifl0,g 064 la$IfK$[$\$ 3 4 5 C ] xx$IfK$[$\$ $If[$\$k$$Ifl0\(dd064 la (,,vvv $If[$\$$IfK$[$\$l$K$L$Ifl0,g 064 la      ! " # $ $,,v $If[$\$l$K$L$Ifl0,g 064 la$IfK$[$\$ $ % & 4 N x xx$IfK$[$\$ $If[$\$k$$Ifl0\(dd064 lax y (,,vvv $If[$\$$IfK$[$\$l$K$L$Ifl0,g 064 la       $,,v $If[$\$l$K$L$Ifl0,g 064 la$IfK$[$\$   L M a p ~~~ $If[$\$[$\$k$$Ifl0\(dd064 la $tttttt(ttttt $If[$\$~$$IflF\( 06    4 la t(t(~$$IflF\( 06    4 la $If[$\$ ! R S T U V trlllrrrrr ~$$IflF\( 06    4 la $If[$\$ 9 : M N O P z { jEHUj+bN UVaJ jEHUjbN UVaJ jpEHUjaN CJUVaJjUmHnHu jU jWEHUV W X Y Z [ \ ] ^   1h/ =!"#$%@=(@Vw`7qۆu86xOY YL w8:!M0qBa$#L` !A .h1+7ql\"Wq7aVR3szv^Ͷv~k<Xn8рDDճgzW:븷8uO=9sf gz-Quڵk=&WѣG{""=z4bF/""X>>>>>>Q"KjޕN2WA|; 3{;>^2WA>X/ w6 wAmAڼyyNqN2WA|; 3{;>^2WA|;j>6 wAmAڼyyjrrdfy'+ wAf >ȝw|r}܈.,Ardfy+ w|;j<>ڼyyjr;>;>ȝwrdfy+ wAf >ȝw|rdfy|WA>;>Xjr;>;>ȝw|Pw|;6 wIf >ȝwrdfy+ wAf >ȝw|rDDm~~r w?^2WA|; >ȝw|ykAmAڼyyjr;^N2WA|; 3{;>^2WA>+ wy|yjr;>;>ȝw|Pw|;$3{;^2WA|; 3{;>^`yLJQۥc?ȝw2WA|; 3{;>rAm|Pw|;6 wAmAڼyyN2WA|; 3{;>^2WA|; >ȝw|ykAmAڼyyjr;^N2WA|; 3{;>^2WA1Rλ+ wAf >ȝw|r^6`>;>ȝw|Pw|;6 wAmAڼy'+ .zɮ\MsϻرcǏAmA-~:}?~luu5ꫯfO>}m0"y{p!ׯBg߽{9+AmA>83*^!5+3{{?igQ!|Pw|{7Q\q~T}!X |Pw|{߿cP}9T|mdkk'|Pw|{{@~9 ;Ε!>>~?'6 vx?uTo=vzWAO?5֫r}xx`+ wG ֫r}t9S̡3Y >ȝwr^ԳgϲefyI}MzIv֭ѣٝ;wW{I oܸ9r$;w\3Fq FJ.rocz^:{Ξ=;uM9*꺺Z޻[YwȊ߉jاrkYϟ\-qF%ޝ/ɽMc&tsZt>}79ogcfR޽{S|w#rСfmzkx+>l 6{>_NK/}/}<5'Nq ^OɓG{sk׮ԤΟA{8oύE=r9_Rw|{3ꏻg_KW}3vّOܻ}{~² rЯY]]W}"3?[>Ƚgk}}]^ |{ý/rP4/{U7 fEM֫>r_ne3ͦ֫>ro2fi|^ |{s}P4&|^ |{Ou0u` az'AY;֒3M/C6 Mu6֫>r_ک Φz'AS{qi|^ |{3|'c=z'A՞tPQi|^ |{=3Tz'A֞eΐϛUWS{&>A'Akܤ}4>S>=]E_ϐ{l)}䞮vgHh6"Q|r&sٖs󦇿Fs#?Ƚe:qi>r/vMJ}l)}x4>S>}UjJfO jW^)ߣuO kW OM>Oܧ]3>i6>r\tK}l)}>^}Y-4>S>Ƚ&}4>S>Ƚ&}4>S>}R{f6>rϰZ=Cj̦A'OgZmifOܧ3i|Ч |b}4>S]}&mO;} +ܤigO>t!E^ж5?l)|6^ڴgM>z t,i|Ч𾳳]~=~vʕرc=?Nn߾=}eMk~4>SUy+?1"<hԦ5?l)|a?~OImZ̦A|{sbk-k~4>SUy?WݻwCUږ5?l)|:߼ys[pbU~>C[i|ЧLϟU4{.]9r>kЖ5?l)|bV_Q_f`޽{+LYgO>T=yCSU{ϯQGLioVnmX̦ähv51_< c9x^ϱ?T=^#_+^/bܹ5v6A|{-x.S-/r!~7k>l)|e+++#0Kw6>2{%ż}.f|4>SM}řI綶ai|Ч{+U}5?l)|&?RsygO>4-ϙM>ܫCsk~4>SMͽs&EfO>49*ΙM>ܫ8gj_t6>CsO}5l)|6򜩩k~4>Sm=9SSi|Чڒ{sEgO>)LM\e̦A|hS)Ι˘M>ж>gj/c6>Cs/󜩉k4>Sm̽s&2fO>t ~sy/k6>Cs/㜩i˚M>8gjfO>=Eϙ潬4>S]}sy/k6>Cr_䜩I˜M>Е=gjkM>Х9gj2gFDիW .ڮRMϱ?t%Yϙٴ} 𡋹reϦA|b<)˞M>ܧ=gjgOܧ9gj2_7>]}sx/{6>]}9SM>Oǟ35{4>S>}9SM>Oǟ35{4>S>}9SM>Oǟ33-Ti|Ч |sx?SxO5}Jej6>rus=l)}>{4>S>}ϙyO9}J?gϙyO9}JWS>}r:4{4>S>}u={4>S>}u3yO=}JO_s"gO jW}T=l)}>{*ϙM>Og]9ӨU̦A'ȦS3_l)}>*ΙFկb6>rvLW1}J/V;9ӨU̦aǍ(tFSպ|@{?9篝i/Rͦ?S>ȽکΙW5}JW;W5}JW;9pfO rk}_M>O.󜩿~i|Ч |{O.㜩~i|Ч |{e3M>O^)_l)}䞾"LygO 9gW=}JWS{s~ճi|Ч |{u9gu̦z'A՞)1UW[{s_lW}^}YΙ~i|^ |{g9gu̦z'AԞi󦫚MO=9Ӆ jMO=9z-i|^ |{'32U_{9kMO]tTz'AS{9/RlW}<ϙ>f` =)^yy>ڼC7s~Vt;v[Am񡣹|XYY677| "*[]|A?=rN~X>'"‡꧟~*dþ}j"jbo1""|8#^7nT"""Zn=}4}vvԩ=ϟΎNj?K(Ci޽ۓDz_?󭭭'BkQ}ܹsH>;zޯ-~ּ~zLgsCkaxF_5+)F] >1?6l {¸\1"au֭Z/i"0WQ_'5f ;ΘE4O}|2%666p̙ǯG99s_ '"gLqݻwoa>uJ^ADz-ļgKϘ}=Dϣ_{@5N>=Rs#ski3ggIx; Y q, uyR>L;a"‡ ""5iQށ,ᯯ+}鯿?HZ{wRݻ)kWM{Nz|{-ʏ}g߉}}vϿg}'\駟DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD*\ac!""CDD.5&{XYY񘈈Hs?ܽ{c""2!Y]]M;R{wj ;wfz:99Lx677.,, R~~c.R흟?x~O _~ _zE*|)~Ljv{E*vcx&>Dq 1Z%b[/^T$?u_ 1?KZa/y+?3rC=D~:ׯ_۷o?ϟ?o{]': Z?sCǹrᆛ7o^zOL|1?n~pu#b}PV|?H ]Y=nk<6T78ӛ7o"R=cy~ yeq155UzDʎs~~au}F}؝17nh{*K\J裏>~2??C߷~Qʃ.<ƷnJ/lɓ':=W>??C//vD+=>{lase;.ϕƽHYLGҸw{]&/e9ϕf{Q??\e2QJ?8GbI˰QJ?8Gb*esށ#KU2,GTnΑإJ}#\iwHR U}t;s$vb_鈪>W:9T/rD+9T/pD+9T/WuD՞+9ԡ/WqD՞+9ԥ/:Jϕ^]ԗ~QJ/{~p.uK {{~p.uK/ {{~p.uK{?{~p.uK7{?{~p.uK'GL:{{~p.ށ#wD|mRٯwH/]~?8Gb}oG~ս?8Gbn:ijj鵦Ias΅gϞn"9IG>E_;>LG~]sZ(jΑE_:=kMjΑE_[{T}{~y/ݯ= G>Ƚ??PӾ;>쳴:RNxIdqzb\׾~[G5(n˛7oҍ7.y͛?k{KǽP=B#Wc~=7|?=}4T x`;}||޽usff&mlldޘt'+l+}掽˵\xx"{{ q髯}/Y[[K̸{?Gz}GܯGOf}}tkOl_הobw}ܱwv\/q>׫p8ˮ}*5\zQ[N}^wp޽u\g;?; v~0w~?xc~;? v~0w/ܱ`s v~0w/ܱ`s;? v~0w/ܱ?xc~;? v~0w/ܱ`s v~0w/ܱ`s;? v~0w0LDqzc`A_c}掝;?;v~}:/ܱ`s;? v~0w/ܱ`s.;? v~0w/ܱ`s;? ?;v~}:/ܱ`s;? v~0w/ܱ`s.;? v~0w/ܱ`s;?DD|'?;v}掝;?;v~`c~;? v~0w/ܱ`s v~0w/ܱ`s;? v~0w/ܱ?xc~;? v~0w/ܱ`s v~0w/ܱ`s;? v~0w/ܱ?xcHvsn/ܱ`s;?v~0wtA_c}掝;?;v~`A_c}];?;v~`A_c}掝;?;v~~0wtA_c}掝;?;v~`A_c}];?;v~`A_c}掝;?;v~?!^O`0w;? v~0w/ܱ?`s/A;?;v~`A_c}掝;?;v`E_c}掝;?;v~`A_c~\s/A;?;v~`A_c}掝;?;v`E_c}掝;?;v~`A_c~\s:9_d3T3Y__OKemm-ao鴺677=""q惕lPCxcjj*mllt9!"R|NȏVז~󘊈T$o߾MWts q*"R#7#=Hu~-{]d!"RkL333= UD:}KR5H5TwzOks?pBDz~3q""RkL~ߒ;^[7)?DyK Ahttp://www.regentsprep.org/Regents/math/geometry/GT4/Lrotate.htmyK http://www.regentsprep.org/Regents/math/geometry/GT4/Lrotate.htmyX;H,]ą'c5Dd   C ArC:\Documents and Settings\NGUYENP\Desktop\ROTATEPIC3.gifb3' M48t4~n' M48t4PNG  IHDRQ0PLTEpo}PO`'0/C񏏚`_o@?Roo__//oOOf??ٟyML^C"!Axw##GG5;;ba},,/_?[Z} 'O<;`z R ',+R}}'('R5Cohg`_kk 5wwTS} 5ML}__AA21`87'('-,`' R kk`RRdd' RCPO RCC 587}5o //54z' ,,??OO__oo##//`{{`mm' 5PPGG@<;0/5aZtRNS@f cmPPJCmp0712HsIDATx^]o(Gd̗IȢ&#6 \qdh: m-"ҫ鰢I;0swEєDw|HBޑ==owI 0A` &X=-5{1_>1=FQTJe$*6oǪdeÊ{qIiWMRNu"-^z(n:8цEL } 76yj:M6u҂r>+2fZ!*;уmhlqP*qez.qT 1Xͩ#y|ژfB&u9G ncsz\t *m*ld<Ls7s(pX̧/T:6+"mX(oUqcNKIS\y xad]poĽQsLUBFa8Bs(7ɩ)*-C7/?dxpE&ڞ:Ōmw.78=&ug}G_1eXuѓlO158UAYnQ_X(;D\b:Tłt lPvw:w.XǂHLW\VdG}.;> ,(+mjT)ClzQ>{!냆`4 fY]x IF/dtȆ]V껰 hH,]h4aGGNRj}> h7D;:n접wXK?=;v:G\4}WvclLFN8źcj%Su,OqCwvȘ;m`y$$3>QНMc+&1@_2hm;X}93?fL*.cɱdto-UCڻn^[m5i6iז8+bYE`h+q:K; 27)zFF{FƘQ‚܃oI'?ɓ'?gPl6f?zcD4)-o_wHoʕ\?맯|gp{ׇD\nd#bog]_?OgUu|5<2$?b;r1[bAE TDuƌV.p.=1ehHQ.l6Mʴ/;|0w'w9ue]l zC8(w!ӟ4I؝@MY;(66vs[ f8k˴?;1v)m`=f7̡Z.L^p:4M!A+.ŋ % N8f̫iA14/=Z"d:(۷nSMs[7˛';0*l°{.T@JTu'Pq]O>AxSQAo2԰)Ϝakc5ƺ#V$SDړxx,,apk@ԎYP 10n|\X*Or@l u" + gi&2- *.ƘT#vpt߄Ci\4-2(tK1l%Ȇn]7? FyaAmRմb4n-kꀋдfK".,TWAҠD Zp6s cXE]Jɐ >7["Uskak%0B G?nG4b E*Ր /ow0Zwىa^øeЈ硜㎐\U5ÈXfݬV( Ԫ`yR!QÑzM7ò/tkD3xU<`SGFYkK;ߐL%l!7+P)IJ72!2DbM:+⋇XXH'7BHLWK qy3_dsGRf+On%ID4hscԤja(jvP18, +3aܔmJ%*M #jW j7l!I)r/w|f\d'78btό]ܤgǨ%qZoa|[us6x-.6c*IQ`V$s$"udnoA1Iݐkbp NsǏcK%H%Fp{ R:#Aψ!JQBIwOFn7Jg%xqI5eFG[Y/䵙7] 3C7ke4Q9n# ,jٜH ,:ai6䴰Iç61+>wH{6tGF>GG`wp ى٬Lg l?Ӊ&V IENDB`DyK Ahttp://www.regentsprep.org/Regents/math/geometry/GT4/PracRot.htmyK http://www.regentsprep.org/Regents/math/geometry/GT4/PracRot.htmyX;H,]ą'cDd\  c $A? ?#" `2i] @c112BYL%bpu?@LCFHGIKJPQMNORSUVWXYZ[\]^_`abcdRoot Entry F0E Data 5WordDocumentiObjectPool ^0_1320837471F^Ole CompObjfObjInfo  !"#$%&'()*+- FMicrosoft Equation 3.0 DS Equation Equation.39qK.\ BLS FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native 5_1320837572 FOle CompObj fObjInfo Equation Native  A_1320837651FppOle  K%P B'L'S' FMicrosoft Equation 3.0 DS Equation Equation.39qKe  HUFCompObj fObjInfoEquation Native 5_1320837675FpqpqOle CompObjfObjInfoEquation Native A FMicrosoft Equation 3.0 DS Equation Equation.39qK%|p H'U'F'Oh+'0  Qh Op*`/M Ma`]Q@@]P@FpA##t] `p021)W2ePdh,s=.Ff 'I1DdH\  c $A? ?#" `2`ߺITц4wH]~`!U`ߺITц4wH*@"H#xcdd``ed``baV d,FYzP1n:B@?b u h7T obIFHeA*L N`A $37X/\!(?71c@`A(-NHq%0eiUQRL>}$? lO0ܞi`{|| NXI9 > '^FV #\*ypAT+F&&\P @ ]` "bDd\  c $A? ?#" `2iy+UV[q$b?mE~`!=y+UV[q$b?m(+H xcdd``> @c112BYL%bpu 1\, K84Dd\   c $A? ?#" `26Gȅhz: `~`!X6Gȅhz: *L H&xcdd``ed``baV d,FYzP1n: lB@?b u  ㆪaM,,He`0 @201d++&1t\> 'Usi#Ɖ 0> *? G$@${ 'WQşL@(\+NBek2¥ \4L=bdbR ,.Ie(ԡ"b> 1Td1TableT@ SummaryInformation(DocumentSummaryInformation8CompObj,j, H T `lt|$Notes Transformations: Rotations supervisorNormal supervisor1Microsoft Word 9.0@ @F#Q@^0K`՜.+,D՜.+,P  hp  CUSD # "Notes Transformations: Rotations Titled 8@ _PID_HLINKSA_SAhttp://www.regentsprep.org/Regents/math/geometry/GT4/PracRot.htmSCAhttp://www.regentsprep.org/Regents/math/geometry/GT4/Lrotate.htmm<v9C:\Documents and Settings\NGUYENP\Desktop\ROTATEPIC3.gif  FMicrosoft Word Document MSWordDocWord.Document.89q i8@8 NormalCJ_HaJmH sH tH <A@< Default Paragraph Font.U`. Hyperlink >*B*phJ^`J Normal (Web)dd[$\$OJPJQJ^J>V@> FollowedHyperlink >*B* ph< z z6"#2Xvxy89Ub| ()*345>?@ABCQk%&'012345C]   !"#$%&4Nxy LMap !RSTUVWXYZ[\]^@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@00000000000000000000000000000000000000@000000000000000@0006  U?A3 $ x  V  b69MOzXX::::/X"$(@Vw`7qۆ"<f"$ biK)_I1CTf@(    |A?. "Picture 16LLjS?@ABQk%&'01234C]   !"#$%4Nxy MapQ@ypP@UnknownG: Times New Roman5Symbol3& : ArialI& ??Arial Unicode MS"hf!fK`Y20 2Q!Notes Transformations: Rotations supervisor supervisor