Unit%15%Packet% % Name:_______________________% Score:%__________/%%

1551:%Geometric%Transformations%–%Translations%and%Reflections%%Remember,%a%transformation%is%a%mathematical%term%for%a%____________________%to%the%figure%or%

graph.%We%will%deal%with%four%main%transformations%in%this%unit.%

15%Slide:%or%__________________% % 25%Flip:%or%________________% 35%Turn:%or%____________________%and%

45%Stretch:%or%______________________%Transformations%create%a%new%figure%called%an%______________,%the%

original%figure%is%called%a%____________________.%

Ex.$1$Identify$the$following$transformations%

%%Today%we%are%going%to%focus%on%two%of%the%transformations,%_________________%and%__________________.%A%

_______________________%moves%every%point%of%a%figure%the%_________%distance%in%the%___________%

directions.%It%maps%or%________%the%points%P%and%Q#%of%the%______________%to%the%points%P’%and%Q’%of%the%

______________.%A%translation%is%___________%motion,%meaning%it%preserves%___________%and%__________%

measure.%%%

On%a%_________________%plane%a%translation%moves%every%________________%point%P(x,#y)%to%an%____________%

point%P(x#+a,#y#+#b)%for%fixed%vales%a%and%b.%A%translation%shifts%a%figure%a%units%_______________________%

and%b%units%__________________.%(Because%x%deals%with%______________%motion%and%y%deals%with%

_______________%motion.)%To%move%an%image%_________%you%will%________%to%the%x,%to%move%it%__________%%

you%will%_______________.%To%move%an%image%_________%you%will%_________%to%the%y,%to%move%it%___________%

you%will%________________.%

Ex.$2$If$the$preimage$point$T(2,$3)$is$translated$right$3$and$up$7,$name$the$point$T’#$in$the$

image.$

$

$

Ex.$3$If$the$preimage$points$T(?1,$4)$and$R($3,?7)$are$translated$left$5$and$down$4,$name$the$

points$T’#and#R’#$in$the$image.$

In%the%coordinate%grid%we%__________________%a%shape%by%moving%its%___________________%the%given%

amount%and%then%redrawing%the%shape.%%

$

Ex.$4$ $ $ $ $ $ $ Ex.$5$%%%%%%%%%%%%%

%%When%we%identify%how%a%shape%has%been%translated%we%want%to%find%how%far%the%vertices%have%been%moved.%%Ex.$6 $ $ $ Ex.$7$$$$$$$$$$$A%__________________%is%a%transformation%that%uses%a%line%like%a%mirror%to%reflect%a%figure.%The%mirror%

line%is%called%the%________%of%____________________.%When%you%reflect%a%point%P%over%line%m%point%P’%on%

the%image%and%point%P%on%the%image%must%be%________________________%to%the%line%m.%

Ex.$8%Draw%the%image%reflected%over%the%given%line:% Ex.$9$

%

%

%

%

%

Coordinate%rules%for%reflections%%

If%point%(a,#b)%is%reflected%in%the%____5axis,%then%the%image%is%the%point%(a,#/b)#

If%point%(a,#b)%is%reflected%in%the%____5axis,%then%the%image%is%the%point%(/a,#b)#

If%point%(a,#b)%is%reflected%in%the%line%y#=#______,%then%the%image%is%the%point%(b,#a)#

If%point%(a,#b)%is%reflected%in%the%line%y#=#______,%then%the%image%is%the%point%(/b,#/a)#

Ex.$10%%% % % % % Ex.$11$

#

#

#

%%%%%%%%%%

To%identify%a%reflection%you%need%to%figure%out%what%_________________%the%shape%is%being%reflected%over.%%Ex.$12$ $ $ Ex.$13$$$$$$$$$$%%A%figure%has%a%%__________%of%symmetry%when%the%figure%can%be%mapped%onto%_________%by%a%reflection%of%that%line.%A%figure%can%have%more%than%one%line%of%symmetry.%Ex.$14$Draw$the$line$of$symmetry$for$each$shape,$how$many$does$each$have?%

15#2:&Geometric&Transformations&–&Rotations&&

A&______________&is&a&transformation&in&which&a&figure&is&turned&about&a&fixed&point&called&the&

_____________&of&___________________.&Rays&drawn&from&the&center&of&

rotation&to&a&point&and&its&image&form&the&____________&of&______________.&&

&

A&_____________&about&point&P&through&an&angle&of&40,&maps&every&point&

Q&in&the&plane&to&a&point&Q’.&A&figure&can&be&rotated&__________________&

and&________________________________.&Assume&all&rotations&are&

________________________&unless&otherwise&noted.&

Ex.$1$Draw$a$ 120 $rotation$of$ ABC $about$point$!P.!

Step&1:&_________________&a&segment&from&P&to&A.&

Step&2:&Draw&a&________&to&form&a& 120 angle&with&PA &&

Step&3:&Draw&______&so&that&PA’&=&PA&

Step&4:&Repeat&for&each&vertex,&draw&the&triangle.&

&

Ex.$2$Draw$a$ 80 $rotation$of$DEFG $about$point$!P.$

&

&

&

&

&

&

You&can&rotate&a&figure&as&much&as&you&want.&If&you&rotate&a&figure& 360 then&the&figure&will&be&

mapped&onto&____________.&We&can&use&coordinate&rules&to&find&the&coordinates&of&a&point&after&a&

rotation&of& 90 ,$ 180 ,$or& 270 about&the&origin.&

Coordinate$Rules$for$Rotations$

When&a&point&(a,&b)&is&rotated&counterclockwise&about&the&origin&the&following&are&true:&

# For&a&rotation&of&_______$(a,&b)&!&(,b,&a)&

# For&a&rotation&of&______&(a,&b)&!&(,a,&,b)&

# For&a&rotation&of&______&(a,&b)&!&(b,&,a)&

&

&

Ex.$3$Graph$the$image$of$the$figure$using$our$coordinate$rules:$

&&&&&&&&&&&&&&&&&A&&rotation&is&a&____________&motion&transformation&which&means&that&it&preserves&congruency.&&&Identifying&a&rotation&

To&identify&a&rotation&means&to&decide&the&__________________,&_____________&of&rotation&and&

_____________________&of&the&rotation.&The&direction&of&the&rotation&can&either&be&_______________________&

or&________________________________.&When&rotating&a&figure&on&a&coordinate&plane&we&most&often&

rotate&about&the&______________________.&

&

Ex.$4$Identify$the$angle$of$rotation,$center$of$rotation$and$direction$of$rotation$for$the$

following:$

$

$

$

$

$

$

$

$

$

Rotational&Symmetry&

A&figure&in&the&plan&has&____________________&symmetry&when&the&figure&can&be&mapped&onto&itself&by&

a&rotation&of& 180 or&less&about&the&__________&of&the&figure.&This&point&is&called&the&_______________&of&

symmetry.&The&rotation&can&be&either&___________________________&or&_________________________.&

&

For&example,&the&figure&below&has&rotation&symmetry,&because&a&rotation&of&either& 90 &or& 180

maps&the&figure&onto&________________,&but&a&rotation&of&__________&does&not.&

&

&

&

&

&

&

Ex.$5$Does$the$figure$have$rotational$symmetry?$If$so,$describe$any$rotations$that$map$the$

figure$onto$itself.&

&

&&&&&&&&&&15#3:&Geometric&Transformations&–&Dilations&and&Combining&Transformations&

&

A&_______________&is&a&transformation&in&which&a&figure&is&________________&or&_________________&by&a&

____________&_____________&k.&A&dilation&makes&shapes&________________&or&_________________&

proportionally.&This&is&how&they&scale&objects.&&

Ex.$1$Decide$if$the$dilation$is$a$reduction$or$an$enlargement$

$

$

&

When&a&shape&is&being&dilated&on&the&coordinate&plan&with&the&origin&as&it’s&center&then&if&P(x,&y)&is&

in&the&pre#image&with&a&scale&factor&of&k&then&the&same&point&in&the&image&will&be&P(kx,&ky).&This&

means&we&________________&our&x&and&y&coordinates&by&the&_________&______________&k.&

&

Ex.$2$If$ ABC has$vertices$A(!&4,!&2),!B(&2,!4)!and!C(&2,!&2)$what$will$it’s$vertices$be$when$

dilated$by$a$scale$factor$of$3?$

$

$

$

$

Ex.$3$If$ABCD has$vertices$A(!8,!&2),!B(&6,!4)!,!C(&2,!&2)!and!D(10,!12)!$what$will$it’s$vertices$

be$when$dilated$by$a$scale$factor$of$1/2?$

$

$

$

Combining&Transformations&

When&combining&transformations&it&is&important&that&we&transform&shapes&in&correct&order.&We&

always&perform&______________________&first,&then&we&can&move&the&shape&around&the&plane.&The&

order&in&which&you&______________,&__________________________,&and&__________________&does&not&matter&as&

long&as&you&always&_________________________&first.&&

&

Ex.$4$Transform$the$following$images$according$to$the$given$directions$

$

Rotate$ 90 counterclockwise$about$the$origin$ $ $ Reflect$across$the$xLaxis$

Translate$up$3$and$left$2$ $ $ $ $ Translate$down$2$and$right$1$

$

&

Secondary*1! ! ! ! ! Name:_________________________________!

In-*Class*15*1!Translations!and!reflections!

!1.!!If!the!preimage!points!T(0,!5)!and!R(!6,*8)!are!translated!left!5!and!down!4,!name!the!points!T’!and!R’!!in!the!image.!!!!2.!!If!the!preimage!points!T(*2,!*8)!and!R(!5,*3)!are!translated!right!3!and!down!6,!name!the!points!T’!and!R’!!in!the!image.!!!!!!3.! !

! 4.!!!!!!!!!!!***For*5-6*identify*the*translation*!!5. !

! 6.!!!!!!!!!!!!!!

7.! !! 8.!!

!!!!!!!!!!!!!!9.!Identify!the!line!that!the!shape!is!being!reflected!over! !

!!!!!!!!!!!!!!!

10.!Determine!whether!the!coordinate!plane!shows!a!reflection!in!the!x)axis,!y)axis!or!neither!

Secondary*1! ! ! ! ! Name:_________________________________!In-*Class*

! ! ! ! ! 15*2!Rotations!1.!Draw!a! 30 !rotation!of! ABC !about!point!!P.!(3pts)!!!!!!!!!2*3!Rotate!the!following!according!to!our!coordinate!rules!for!rotations!2.! ! ! 3.!!!!!!!!!!!!!!4*5!Identify!the!angle!of!rotation,!center!of!rotation!and!direction!of!rotation!for!the!following:!!!!!!!!!!!6*8!For!the!following!identify!the!rotational!symmetry

!

Review&Fill&in&the&blank&using&the&words&dilation,(reflection,(rotation,(or&translation.&

Write&answers&here.&

1.&A&transformation&that&moves&all&points&the&same&distance&in&the&same&direction&is&called&a&______________________.&

1.&

2.&A&transformation&that&moves&a&figure&over&a&line&to&create&an&image&that&is&the&same&distance&from&the&line&is&called&a&_______________________.&&&

2.&

3.&A&transformation&that&moves&all&points&of&a&figure&around&a&fixed&point&in&the&same&angle&and&direction&is&called&a&_______________________.&

3.&

4.&A&transformation&that&enlarges&or&reduces&the&original&figure&is&called&a&________________________.&

4.&

Write&a&rule&that&describes&each&transformation.& Write&answers&here.&&5.&&&&&&&&&&

5.&

6.(((((((((&

6.&

7.&&&&&&&&&&&

7.&

8.&&&&&&&&&

8.&

&&

Graph&the&image&of&the&figure&using&the&transformation&given.&9.&Translation&4&units&left&and&1&unit&up.& & & 10.&Translation −2,−2 .&&

&&&&&&&&&&&&&&&

11.&Reflection&across&! = −1.& & & & 12.&Rotation&180°&about&the&origin.&&&&&&&&&&&&&&&&

13.&Reflection&across&! = !& & & & 14.&&Dilation&of&ABC,&(0,&1)&(P4,&6),&(8,&P1)&by&4&