# Defining Rotations

# Defining Rotations

##### 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 $B$?

##### 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 $D'$: