# Defining Rotations

ID: jovik-nunod
Illustrative Math
Subject: Geometry
Grade: 9-12

# Defining Rotations

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##### Problem 1

1) Draw the image of quadrilateral ﻿$ABCD$﻿ when rotated ﻿$120^{\circ}$﻿ counterclockwise around the point ﻿$D$﻿.

##### Problem 2

2) There is an equilateral triangle,﻿$ABC$﻿, inscribed in a circle with center ﻿$D$﻿. What is the smallest angle you can rotate triangle ﻿$ABC$﻿ around ﻿$D$﻿ so that the image of ﻿$A$﻿ is ﻿$B$﻿?

a) $60^{\circ} \text{ }$b) $90^{\circ} \text{ }$c) $120^{\circ} \text{ }$d) $180^{\circ}$
##### Problem 3

3) Which segment is the image of ﻿$AB$﻿ when rotated ﻿$90^{\circ}$﻿ counterclockwise around point ﻿$P$﻿?

##### Problem 4

4) The semaphore alphabet is a way to use flags to signal messages. Here's how to signal the letter Q. Describe a transformation that would take the right hand flag to the left hand flag.

##### Problem 5

5) Below are 2 polygons.

Select all sequences of translations, rotations, and reflections below that would take polygon ﻿$P$﻿ to polygon ﻿$Q$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) Rotate ﻿$180^{\circ}$﻿ around point ﻿$A$﻿.

b) Translate so that ﻿$A$﻿ is taken to ﻿$J$﻿. Then reflect over line ﻿$BA$﻿.

c) Rotate ﻿$60^{\circ}$﻿ counterclockwise around point ﻿$A$﻿ and then reflect over the line ﻿$FA$﻿.

d) Reflect over the line ﻿$BA$﻿ and then rotate ﻿$60^{\circ}$﻿ counterclockwise around point ﻿$A$﻿.

e) Reflect over line ﻿$BA$﻿ and then translate by directed line segment ﻿$BA$﻿.

##### Problem 6

6) Draw the image of figure ﻿$ABC$﻿ when translated by directed line segment ﻿$u$﻿. Label the image of ﻿$A$﻿ as ﻿$A'$﻿, the image of ﻿$B$﻿ as ﻿$B'$﻿, and the image of ﻿$C$﻿ as ﻿$C'$﻿.

7) Explain why the line containing ﻿$AB$﻿ is parallel to the line containing ﻿$A'B'$﻿.

##### Problem 7

8) There is a sequence of rigid transformations that takes ﻿$A$﻿ to ﻿$A'$﻿, ﻿$B$﻿ to ﻿$B'$﻿, and ﻿$C$﻿ to ﻿$C'$﻿. The same sequence takes ﻿$D$﻿ to ﻿$D'$﻿. Draw and label ﻿$D'$﻿: