unit 1 test review transformations in the coordinate plane...
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Unit1TestReview:TransformationsintheCoordinatePlane
1.Asshowninthediagrambelow,whenhexagonABCDEFisreflectedoverlinem,theimageishexagonA’B’C’D’E’F’.
Underthistransformation,whichpropertiesarepreserved?distance,angles,orientation,area
2.Checkallofthebelowseriesoftransformationsthatwillresultinacongruentimage.
• Atranslationfiveunitsupfollowedbyadilationusingascalefactorofone• A270degreecounterclockwiserotationfollowedbyareflectionovertheliney=0• A90degreerotationfollowedbyareflectionovertheliney=x• Areflectionoverthex-axisfollowedbyadilationusingascalefactorof2
3.Fillintheblankstomakestatementsthatwillmapthequadrilateralgraphedbelowontoitself.
• Reflectionovertheline𝑦 = 1• 180degreerotationaboutthepoint(−1, 1)• Reflectionovertheline𝑥 = 1
4.Thetransformation(𝑥, 𝑦) ⟶ −𝑥,−𝑦 willmaptriangleABCtotriangleA’B’C’.
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5.Listtheallthedegreesofrotations(lessthan360)thatwillmapthefigurebelowontoitself.
360 ÷ 5 = 72°
72°, 144°, 216°, 288°
6.Ifthesegmentbelowisreflectedovertheliney=1,thentranslated3unitstotheleft,thecoordinatesoftheendpointsoftheimageare(−4,−6)and(2, 0).
7.QuadrilateralJKLManditsreflectedimageareshown.Fillintheblanks
• Theimageshowstheresultofareflectionacrosstheline𝑦 = 𝑥.• ThepaththatpointLtakestoL’isperpendiculartothelineofreflection.• Eachpoint(x,y)onquadrilateralJKLMmapstoapoint 𝑦, 𝑥 onitsimage.• CorrespondingsidesofquadrilateralJKLManditsimagearenotparallel.•
8.ThetrapezoidbelowistranslatedsuchthatA’=D.ThecoordinatesoftheimageB’afterthetranslationis(0, 2).
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9.CheckallofthebelowtransformationsontriangleABCthatproducesanimagecongruenttotriangleABC.
• reflectionacrossy=x • translation3unitsdownand4unitstotheright• dilationbyascalefactorof1.5 • clockwiserotationof270degrees
10.Findaseriesoftransformationsthatmaps ABC to RST .
Answersmayvary.
Reflect∆𝐴𝐵𝐶acrossthey-axis,
thentranslateit2unitsleftand
5unitsdown
11.TheimageofpointQafteracounterclockwiserotationof270degreesabouttheoriginis(3, −2).
𝑅9:;° 𝑥, 𝑦 = (𝑦,−𝑥)
𝑄 2, 3
𝑄>(3, −2)
12.Thefunction𝑅?@A 𝑥, 𝑦 = (𝑦, 𝑥)describesthetransformationofrectanglePQRStoP’Q’R’S’.
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13.ThegraphbelowshowsparallelogramTEAM.AcongruentparallelogramT’E’A’M’hascoordinates'( 7,0), '( 3,0), '( 4, 3)E A M ,and𝑇>(8, 3).?
14.Listallofthedegreesofrotations(lessthan360)thatwillmapthepreimagetotheimagebelow.
90°, 270°
15.Thefunction𝑇 𝑥, 𝑦 = (𝑥 + 7, 𝑦 − 7)describesthetransformationgraphedbelow.
16.IftrapezoidDEFGbelowisreflectedsothatE’=(5,-5),thelineofreflectionis𝑦 = −1.
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17.Thefunction(𝑥, 𝑦) → −𝑦, 𝑥 describestherotation.
18.Thesingletranslation 𝑥, 𝑦 → 𝑥 + 4, 𝑦 − 4 accomplishesthesametranslationasthefollowingseriesoftranslations: 𝑥, 𝑦 → 𝑥 + 5, 𝑦 − 3 followedby 𝑥, 𝑦 → 𝑥 + 2, 𝑦 − 4 followedb 𝑥, 𝑦 → 𝑥 − 3, 𝑦 − 3 y.
19.ListthecoordinatesfortheimageofpointP(-2,4)aftereachofthefollowingreflections.
• PointPisreflectedoverthey-axis.(2, 4)• PointPisreflectedoverthex-axis.(−2,−4)• PointPisreflectedovertheliney=x.(4, −2)
20.
• TriangleDisa270degreecounterclockwiserotationoftriangleC.
• TriangleCisa90degreeclockwiserotationoftriangleB.• TriangleCisa180degreerotationoftriangleA.• TriangleBisa270degreeclockwiserotationoftriangleC.
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21.Inthegraphbelow∆𝐴𝐵𝐶 ≅ ∆𝐴′𝐵′𝐶′.Explainusingtransformationshowyouknowthetrianglesarecongruent.Listthetransformationorseriesoftransformations.Alsolistcorrespondinganglesandsidesthatarecongruent.(Writeincompletesentences.)
∆𝐴𝐵𝐶wasrotated270°counterclockwise.
𝐴𝐵 ≅ 𝐴′𝐵′∠𝐴 ≅ ∠𝐴′
𝐴𝐶 ≅ 𝐴′𝐶′∠𝐵 ≅ ∠𝐵′
𝐵𝐶 ≅ 𝐵′𝐶′ ∠𝐶 ≅ ∠𝐶′
22.Considerthefollowingtrianglesgraphedbelow.(Writeincompletesentences.)
A.Whatseriesoftransformationswillmaponeofthegraphedtrianglesontotheothertriangle?
Reflectacrossthey-axis,thentranslate6unitsdown.
B.Dothetransformationsensurethatthetrianglesarecongruent?Explain.
Yes,reflectionsandtranslationspreservetheshapeandsize.
23.Liamsaysthat GHJ canbemappedto XYZ withaseriesofrigidmotiontransformations.Ishecorrect?Isso,giveaseriesoftransformationsthatworks.Ifnot,explainwhynot.(Writeincompletesentences.)
No,Liamisnotcorrect.𝐺𝐽in∆𝐺𝐻𝐽isonly4unitslongversusits“correspondingside”of𝑋𝑍in∆𝑋𝑌𝑍whichis5unitslong.
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24.TrianglesABCandDEFarecongruent.
A.WriteafunctiontodescribethetranslationthatmapstriangleABCtotriangleDEF.(𝑥, 𝑦) ⟶ (𝑥 + 4, 𝑦 − 9)
B.WriteafunctiontodescribethetranslationthatmapstriangleDEFtotriangleABC.(𝑥, 𝑦) ⟶ (𝑥 − 4, 𝑦 + 9)
25.Listallthesingletransformationsthatwillmapthefigureontoitself.Rotationsshouldbeclockwiseandlessthan360degrees.Namealllinesofreflection.(Writeincompletesentences.)
90°, 180°, 270°
Linesofreflection:𝑥 = 0, 𝑦 = 0, 𝑦 = 𝑥, 𝑦 = −𝑥