[PACKET 8.3: ROTATIONS] 1

 

Rotations are exactly as you would expect: a transformation that turns an image around a given point. When we are graphing, that point will always be the origin (0,0). We usually rotate in the same direction that we number the quadrants: ____________________. If you are asked to rotate clockwise, find the equivalent rotation counterclockwise. (More later…)

ΔABC is rotated 90o ΔABC is rotated 90o ΔABC is rotated 90o about point B about point A about point C Rules for rotating _________________________________ about the origin:

 Please  keep  in  mind:

A  rotation  of  270o COUNTERCLOCKWISE is equivalent to a rotation of _____________________! A rotation of 360o in either direction maps each preimage onto itself.

 Find  the  coordinates  of  ΔA(2, 1), B(3, -1), C(-4, 0) after a rotation of 90o counterclockwise about the origin.  

Rule Abbreviation Transformation Rotation of 90o about the origin

90R ° (x, y) à Rotation of 180o about the origin

180R ° (x, y) à

Rotation of 270o about the origin 270R °

(x, y) à Rotation of 360o about the origin

360R ° (x, y) à

Write your questions here!

Name______________________

A'C'

C

BA B'

A' C

BAC'

B'

C

BA

2   PACKET 8.3: ROTATIONS  

-­‐5 5

6

4

2

-­‐2

-­‐4

 Find  the  coordinates  of  ΔD(-2, 5), E(0, 4), F(-4, -3) after a rotation of 180o counterclockwise about the origin.

 Find  the  coordinates  of  ΔG(4, -7), H(-2, 4), F(-1, 0) after a rotation of 90o clockwise about the origin.  

a. Graph trapezoid TRAP where T(0, 4), R(-2,1), A(-5,1), and P(-5,4). b. Graph T’R’A’P’, the image of TRAP after 0270R . c. Graph kite KITE where K(-3, -3), I(-1, -3), T(-1, -1) and E(-4, 0).

d. Graph K’I’T’E’, the image of KITE after 090R .                                        

 

An object has ____________________if there is a center point around which the object is rotated a certain number of degrees and the object looks the same. Examples:

Write your questions here!

[PACKET 8.3: ROTATIONS] 3

Which of the following letters have rotational symmetry? Which have reflectional symmetry?

Now

, sum

mar

ize

your

no

tes

here

! Write your questions here!

Worksheet by Kuta Software LLC

©7 42R0B1I3g EKcuptaa1 TSPoSfFtHwTabr9eo BLcL9C2.A j BA2lule UrViQgth4tqsZ Prbe8s8earYvVemdP.p Practice 8.3Graph and label the image of the figure using the transformation given.

1) rotation 90° counterclockwise about theorigin

x

y

Z

T X

D

2) rotation 180° about the origin

x

y

T

M

N

Find the coordinates of the vertices of each figure after the given transformation.

3) rotation 90° clockwise about the originG(, ), B(, ), U(, )

4) rotation 90° clockwise about the originR(, ), F(, ), H(, )

5) rotation 180° about the originI(, ), F(, ), C(, )

6) rotation 90° counterclockwise about theoriginI(, ), X(, ), Q(, )

-1-

Worksheet by Kuta Software LLC

Graph the image and the preimage of the figure using the transformation given.

7) rotation 90° counterclockwise about theoriginG(, ), B(, ), J(, )

x

y

8) rotation 180° about the originD(, ), S(, ), Q(, )

x

y

Graph the image and the preimage of the figure using the transformation given.

9) rotation 90° clockwise about the origin

x

y

S

J

F

10) rotation 90° counterclockwise about theorigin

x

y

X

U

F

J

-2-

Worksheet by Kuta Software LLC

Find the coordinates of the vertices of each figure after the given transformation. Then graph thereflection.

11) rotation 90° clockwise about the origin

x

y

U

F

M

12) rotation 180° about the origin

x

y

A

E

R

V

13) rotation 90° counterclockwise about theoriginU(, ), I(, ), C(, ), E(, )

14) rotation 180° about the originF(, ), D(, ), V(, ), E(, )

Tell the type of rotation that describes each transformation.

15)

x

y

L

A

U

F

L'A'

U'

F'

16)

x

y

Z

G

H

B

Z'

G'

H'

B'

17) F(, ), N(, ), V(, ), U(, ) toF'(, ), N'(, ), V'(, ), U'(, )

18) Q(, ), A(, ), I(, ), E(, ) toQ'(, ), A'(, ), I'(, ), E'(, )

-3-

4   PACKET 8.3: ROTATIONS  

 1.    Find  the  coordinates  of  ΔC(-2, 3), A(-3, 4), T(2, 0) after a rotation of 90o counterclockwise about the origin.    2.    Graph  the  image  and  the  preimage  of  the  figure  after  a  rotation  of  90o  clockwise  about  the  origin.                  3.    Name  3  letters  that  do  not  have  rotational  symmetry.      4.  Name  3  letters  that  do  have  rotational  symmetry.        5.   Sully  has  a  lot  of  hobbies,  but  he  likes  nothing  more  than  his  paper-­‐folding  club:  Coreygami!  Currently  the  club  has  (18,987,310)0  members.    For  this  application  problem,  you  will  get  a  chance  to  join  Coreygami.    To  join,  you  must  create  a  figure  with  rotational  symmetry  using  Coreygami.  The  choice  is  yours:  you  can  certify  yourself  as  an  "Amateur,"  "Professional,"  "Warrior,"  or  "Supreme-­‐Jedi-­‐Master"  Coreygamist.    Those  that  complete  the  "Supreme  Jedi  Master"  receive  a  personalized  laser-­‐printer-­‐signed  certificate  from  the  Algebros.          To  complete  the  application  task,  go  to  the  8.3  section  page,  and  choose  one  of  the  tasks  below  the  lesson  video.  You  must  follow  the  directions  carefully.  After  you  have  completed  your  application  task,  answer  the  following  questions:      

a. Your  origami  product  has  several  "points"  of  symmetries.    How  many  "points"  are  there?    

b. Divide  360  degrees  by  the  number  of  symmetrical  "points"  in  your  product.  This  is  called  the  angle  of  rotation.  What  is  the  angle  of  rotation  of  your  product?  

   

c.   Write  your  name  on  your  creation.  Your  masterpiece  will  be  displayed  for  all  to  admire!