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 ΔXNJ( ) ___________________________________________________________________________________

_________________________________________________________________________________________________. _________________________________________________________________________________________________. _________________________________________________________________________________________________.

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 ΔHJL( )

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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