1

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Lesson4:Rotations • Animagecanberotatedabouta

___________________________point.¢ Thebladesofafanrotateabout

afixedpoint.Vocabulary:• _____________________________-

apointaroundwhichafigureisrotated

• _____________________________-whichwayafigureisrotated.

1. Thisisatriangleata0°or360°rotation.

Weusethisasourstartingpoint.

Besuretowatchthechangeinthesignsoftheorderedpairsaswemovethroughtheotherquadrants2. Noticethatwitha90°rotation(quarter

rotation)theimagetrianglemovedtoquadrant2orquadrant4.Afigurecanrotateclockwiseorcounterclockwise.

OriginalCoordinates:A(3,6) B(3,2) C(6,2)90°ClockwiseRotation:𝐴<(,) 𝐵<(,) 𝐶<(,)90°CounterclockwiseRotation:𝐴<(,) 𝐵<(,) 𝐶<(,)Thesignsofthey-coordinatesdidnotchangebutthex-coordinatesdid.Also,thex&ycoordinatesswitchedspots.(Every90°flipthecoordinateandcheckthesignthatshouldbeinthequadrantyouarein)

3. Noticethatwitha180°rotation(halfrotation)thefiguremovedthequadrant3.(or90°andthen90°again)

OriginalCoordinates:A(3,6) B(3,2) C(6,2)180°Rotation:𝐴<(,) 𝐵<(,) 𝐶<(,)Theonlydifferencebetweentheoriginaltriangleandtheimagetriangleisthesignchangeonallofthecoordinates.Thenumbers,however,didn’tflip-flopbutratherstayintheiroriginalposition.

4. Theoriginaltrianglehasnowrotated270°(¾rotation)fromitsoriginalposition.(or90°counterclockwise)

OriginalCoordinates:A(3,6) B(3,2) C(6,2)90°ClockwiseRotation:𝐴<(,) 𝐵<(,) 𝐶<(,)90°CounterclockwiseRotation:𝐴<(,) 𝐵<(,) 𝐶<(,)ThesignsontheycoordinatesONLYhavechangedandthexandycoordinateshaveflip-flopped.

a. Whenafigureisrotated90°counterclockwiseabouttheorigin,multiplythey-coordinateby-1andswitchthex-andy-coordinates.

(x,y)à_______________________b. Whenafigureisrotated180°aboutthe

origin,multiplybothcoordinatesby-1.(x,y)à_______________________

c. Whenafigureisrotated270°

counterclockwise(90°clockwise)abouttheorigin,multiplythex-coordinateby-1,thenswitchthex-&y-coordinates. (x,y)à_______________________

5. DrawtheimageofABCDundera

180°clockwiserotationabouttheorigin.

6. Rotatethefollowingimage90°clockwiseabouttheorigin

7. Rotatetheimage270°clockwisearoundtheorigin

Findthecoordinatesoftheverticesofeachfiguregiventherotation:

8. Rotation90°clockwiseabouttheorigin𝑍 −1,−5 , 𝐾 −1, 0 , 𝐶 1, 1 , 𝑁(3, −2)

_________________________________

9. Rotation180°abouttheorigin𝑆 1,−4 ,𝑊 1, 0 , 𝐽 3, −4

Writearuletodescribeeachrotation:

10. ______________

11. ____________

12. HexagonDGJTSRisshownbelow.IdentifythenewcoordinatesofpointTaftereachofthefollowingrotations:

a. 0°or360°=________________b. 90°clockwise=_____________c. 90°counterclockwise=_______d. 180° =____________________e. 270°clockwise=____________f. 270°counterclockwise=______

1

LESSON4-PRACTICEGraphthefollowingfigurewiththeinformationprovided.1. Rotate180°clockwise

2. Rotate90°clockwiseabouttheorigin

3. Rotate270°clockwiseabouttheorigin

4. Rotate180°counterclockwise

5. Rotate90°counterclockwise

Writetheruleforthefollowingtransformation

6. _________________________________

7. _________________________________

8. _________________________________

9. HexagonDGJTSRisshownbelow.IdentifythenewcoordinatesofpointRaftereachofthefollowingrotations:

a. 0°or360°=________________

b. 90°clockwise=_____________

c. 90°counterclockwise=_______

d. 180° =____________________

e. 270°clockwise=____________

f. 270°counterclockwise=______

10. Rotation180°abouttheorigin𝑍 1,−3 , 𝐾 8, 1 , 𝐶 0, −6 , 𝑁(10,−4)

_________________________________

11. Rotation270°counterclockwise

𝑆 3,−7 ,𝑊 −6,−1 , 𝐽 4, 8

_________________________________

12. QuadrilateralKSJWisshownbelow.IdentifythenewcoordinatesofpointSaftereachofthefollowingrotations:

a. 0°or360°=________________

b. 90°clockwise=_____________

c. 90°counterclockwise=_______

d. 180° =____________________

e. 270°clockwise=____________

f. 270°counterclockwise=______

13. TriangleCLTisshownbelow.IdentifythenewcoordinatesofpointTaftereachofthefollowingrotations:

a. 0°or360°=________________

b. 90°clockwise=_____________

c. 90°counterclockwise=_______

d. 180° =____________________

e. 270°clockwise=____________

f. 270°counterclockwise=______