3.10 Rigid Transformations Sequence of Transformations Rigid Transformations: Sequence of Transformations ... Read the sentence ... 3.10 Rigid Transformations: Sequence of Transformations

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  • 3.10 Lesson Name (print first and last) _____________________________________ Per_____ Date: 10/29 due 10/31 3.10 Rigid Transformations: Sequence of Transformations Geometry Regents 2013-2014 Ms. Lomac SLO: I can perform a sequence of transformations on a given figure using a straightedge and compass and explain how and why the construction of the sequence results in the final image. (1) R is the midpoint of ST . Answer each question about the diagram. (a) When S is rotated 180 around R it maps to point T because . . . _______________________________________________________________________ (b) When N is rotated 180 around R it maps to point U because . . . _______________________________________________________________________ (c) SN TU because . . . ________________________________________________________________________________ (d) Do you think NSR UTR ? _______ because. . . ________________________________________________ _________________________________________________________________________________________________. (2) Construct each transformation

    (a) Rotate M 90 around point E (RE, 90 ) (b) Reflect point H across line m. (rm) (c) Translate point Q along vector VA ( TVA )

    (3) In problem 2, there are abbreviations for each transformation in parentheses. Write out what each transformation abbreviation means below.

    (a) TSQ __________________________________________________________________________________

    (b) RG ,35 ______________________________________________________________________________ (c) rXW __________________________________________________________________________________

    E M

    U R

    S

    T

    N

    H

    m V Q

    A

  • 3.10 (4) A sequence or composition of transformations is when a figure undergoes multiple transformations. Describe each composition of transformations below using the terms reflection, rotation, and translation. Estimate degrees of a rotation and direction and distance of a translation. (a) (b) (c) (d)

    ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

    ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

    ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

    ___________________ ___________________ ___________________ ___________________ ___________________ ___________________

    (5) Reading and writing transformations. (a) Descriptions of compositions of transformations are stated:

    The reflection across line m of a translation along vector AB of point Q. Which do you think happens first, the reflection, or the translation? _____________________ because __________

    ____________________________________________________________________________________________ (b) Read the statement:

    Anthony took a picture of the drawing of his family. Which do you think happens first, the picture or the drawing? ___________________ because _______________ ____________________________________________________________________________________________ (c) Read the sentence from part (a) again.

    The reflection across line m of a translation along vector AB of point Q. Which happens first, the reflection, or the translation? _____________________ Did your answer change? ______ Why/why not? ________________________________________________________________________________

    (6) Compositions of transformations are written THA RC ,45 (YZ ). This is read the transformation along vector HA of the rotation 45 around point C of segment YZ. Based on your work in problem #5, Which happens first, the translation or the rotation? _____________________________ because __________________________________________________ ____________________________________________________________________________________________

  • 3.10 (7) Use the abbreviation examples from problem #3 and the order of compositions from #5 & #6 to describe each composition of transformations and then write the abbreviation for it. (a) Abbreviation: ________________________________

    Description: ________________________________________________ __________________________________________________________ __________________________________________________________

    (b) Abbreviation: ________________________________

    Description: ________________________________________________ __________________________________________________________ __________________________________________________________

    (8) Describe with as much detail as possible the composition of transformations that map PQR to XYZ. You may want to add letters to the in-between steps to make your explanation easier. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________.

    P

    X

    Z

    Y

    X'

    Z'

    Y'

    X'' Z''

    Y'' V

  • 3.10 (9) Construct each composition of transformations.

    (a) TAB r XY( )

    (b)

    rm RC , 60 Q( )

    Q

    C

    X Y l

    A B

    m

    60

  • 3.10 day 1 HW Name (print first and last) _____________________________________ Per_____ Date: 10/29 due 10/30 3.10 Rigid Transformations: Sequence of Transformations Geometry Regents 2013-2014 Ms. Lomac (1) Describe each transformation. Circle the part of the transformation that happens first.

    rCD r

    MT XNJ( ) ___________________________________________________________________________________

    _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________.

    TWB RJ ,42 LU( ) ___________________________________________________________________________________ _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________.

    RC ,25 rl F( ) ___________________________________________________________________________________ _________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________. (2) Construct a copy of angle S. (3) Bisect angle S' in problem number 2.

    S

  • 3.10 day 2 HW Name (print first and last) _____________________________________ Per_____ Date: 10/30 due 10/31 3.10 Rigid Transformations: Sequence of Transformations Geometry Regents 2013-2014 Ms. Lomac (1) Construct

    RR,180 TAB HJL( )

    J

    L

    A

    B

    H

    R

  • 3.10 Exit Ticket Name_________________________________________Per______ Write the abbreviation and Description for the composition of transformations

    Abbreviation: ________________________________ Description: _______________________________________________ ________________________________________________________ __________________________________________________________

    3.10 Day 1 Exit Ticket Name_________________________________________Per______ Write the abbreviation and Description for the composition of transformations

    Abbreviation: ________________________________ Description: _______________________________________________ ________________________________________________________ __________________________________________________________

    3.10 Day 1 Exit Ticket Name_________________________________________Per______ Write the abbreviation and Description for the composition of transformations

    Abbreviation: ________________________________ Description: _______________________________________________ ________________________________________________________ __________________________________________________________

    3.10 Day 1 Exit Ticket Name_________________________________________Per______ Write the abbreviation and Description for the composition of transformations

    Abbreviation: ________________________________ Description: _______________________________________________ ________________________________________________________ ________________________________

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