Name_______________________ Date________ Transformations Review for Test Geometry

Ms.Talhami1

Transformation Notation Examples Rules

Translation

Reflection

Rotation

Dilation

SomeOtherVocabularySymmetry,LineofSymmetry,PointSymmetry,RotationalSymmetry(Order&Angle),Orientation,RigidMotion,Isometry(Isometric),Pre-Image,Image,Prime,Sequence(Composition)ofTransformations

Ms.Talhami

2

1.Atransformationwasusedtomap ABCΔ ontoitsimage ' ' 'A B CΔ .Whichofthefollowingtransformationswouldnotguaranteethat ' ' 'A B CΔ hasthesamesizeandshapeas ABCΔ ?

a)atranslation b)arotationc)adilation d)areflection

2.Whichofthefollowingisnotapropertyofallrigidmotions? a)anglesarepreserved b)thelengthofalinesegmentandthelengthofitsimageareequal c)linesaremappedtoparallellines d)theimagesoftwoperpendicularlineswillbethemselvesperpendicular3.Thepoint ( )1, 8 wastranslatedinthecoordinateplaneandthenreflectedacrossthex-axis.Itsfinalimage

washadthecoordinates ( )4, 3− .Whichofthefollowingbestdescribesthetranslationthatoccurred? a)ashiftof3unitstotherightand11unitsdown b)ashiftof8unitsleftand2unitsdown c)ashiftof3unitstotherightand5unitsdown d)ashiftof2unitsleftand4unitsup4.Whichofthefollowingrotationsofaregulardecagonaboutitscenterwouldnotmapitontoitself? a)72 b)252 c)174 d)324 5.IsoscelesrighttriangleABCisshownbelowwiththemidpointofhypotenuse BC markedasD.Whichof

thefollowingtransformationswouldmap ABCΔ ontoitself? a)a180 rotationaboutD

b)areflectionacross AC

c)aclockwiserotationof90 aboutpointA

d)areflectionacross AD 6.Inthefollowingdiagram, ABCΔ hasbeentransformedinto '' '' ''A B CΔ bytheuseofasequenceof

transformations. a)Giveonesuchsequenceoftransformationsthatwouldmap

ABCΔ to '' '' ''A B CΔ . b) Whydoesthissequenceprovethatthetwotrianglesare

congruent?

Ms.Talhami

3

7.TriangleABCisshownbelowwithverticesat ( )3, 2A − , ( )3, 6B − ,and ( )9, 2C − . a) Draw ' ' 'A B CΔ , the image of ABCΔ , after a 90

counterclockwise rotation about the origin. Givethecoordinatesoftheverticesof ' ' 'A B CΔ below.

b) If ' ' 'A B CΔ is mapped to '' '' ''A B CΔ using a

translationsuchthatitsverticesareat ( )'' 3, 4A − − ,

( )'' 1, 4B − and ( )'' 3, 2C − , give a rule for thistranslation.

8.Inthediagramshown, AE andBD bisecteachotheratC.Givearigidmotionthatwouldmap ABCΔ onto

EDCΔ .Explainwhythisshowsthatthetwotrianglesarecongruent.9.