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    Notes in Rotations

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    hfej

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    Notes in Rotations

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    50 views4 pages

    Notes in Rotations

    Uploaded by

    hfej

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 4

    Rotations

     
     
    A  rotation  is  a  transformation  that  turns  a  figure  about  a  fixed  point  called  the  center  of  rotation.    An  
    object  and  its  rotation  are  the  same  shape  and  size,  but  the  figures  may  be  turned  in  different  
    directions.      Rotations  can  occur  in  either  a  clockwise  or  counterclockwise  direction.    The  figure  does  
    not  change  size.  
     
     
     

                                 
     
     
     

     
     
    Notice  that  a  rotation  of  180°  about  the  origin  is  the  same  as  a  point  reflection.    A  rotation  of  360°  
    would  match  the  image  with  its  preimage.    A  positive  angle  of  rotation  turns  the  figure  
    counterclockwise,  and  a  negative  angle  of  rotation  turns  the  figure  in  a  clockwise  direction.  
     
    Counterclockwise   Clockwise   Rule  
    𝑅!"   𝑅!!"#   (𝑥, 𝑦) → (−𝑦, 𝑥)  
    𝑅!"#   𝑅!!"#   (𝑥, 𝑦) → (−𝑥, −𝑦)  
    𝑅!"#   𝑅!!"   (𝑥, 𝑦) → (𝑦, −𝑥)  
     
       
    Notice  that  degree  movement  on  a  unit  circle  goes  in  a  counterclockwise  direction.    
    You  will  want  to  remember  the  layout  of  the  unit  circle  when  you  are  graphing  figures  and  their  
    rotations.  

     
     
     
     
    Examples  
    1.    What  is  the  image  of  the  point  (6, −3)  under  the  rotation  𝑅!"  about  the  origin?  
     
     
     
    2.    What  is  the  image  of  the  point  (−5, 10)  under  the  rotation  𝑅!"#  about  the  origin?  
     
     
     
    3.    What  is  the  image  of  the  point  (2,4)  under  the  rotation  𝑅!!"  about  the  origin?  
     
     
     
    4.    A.    Graph  and  label  ∆𝐽𝐾𝐿  with  vertices  J(2,  2),  K(4,  –5),  and  L(–1,  6)    
    B.    Graph,  label  and  state  the  coordinates  of  ∆𝐽′𝐾′𝐿′,  the  image  of  ∆𝐽𝐾𝐿  after  a  rotation  of  180°      
               about  the  origin.  

     
    5.    A  rectangle  is  plotted  on  the  coordinate  plane  below.    Draw  the  image  of  this  rectangle  after  the  
    rotation  𝑅!!" .  

       
     
    6.    A  triangle  is  plotted  on  the  coordinate  plane  below.    Draw  the  image  of  this  triangle  after  the  rotation  
    𝑅!" .  

     
     
    7.    A  clockwise  rotation  of  90°  is  the  same  as  a  counterclockwise  rotation  of  ____________.  
     
    8.    A  clockwise  rotation  of  180°  is  the  same  as  a  counterclockwise  rotation  of  ____________.  
     
    9.    A  clockwise  rotation  of  270°  is  the  same  as  a  counterclockwise  rotation  of  ____________.  
     
    10.  A  rotation  of  360°  is  the  same  as  a  rotation  of  ____________.  
     
    11.    The  drawing  below  shows  a  rotation  of  ____________  or  ______________.  
     
    NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 13 M1
    GEOMETRY

    Name ___________________________________________________ Date____________________

    Lesson 13: Rotations

    Exit Ticket

    Find the center of rotation and the angle of rotation for the transformation below.

    Lesson 13: Rotations


    Date: 8/9/13

    This work is licensed under a


    © 2013 Common Core, Inc. Some rights reserved. commoncore.org
    Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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