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’.

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).

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’.

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.

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.

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.

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