name date transformations review for test geometry · translation reflection rotation dilation some...
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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.