# Incorporating Rotations

# Incorporating Rotations

##### Problem 1

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

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

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

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

##### Problem 2

2) 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 left hand flag to the right hand flag.

##### Problem 3

Match each directed line segment below with the image of Polygon $P$ being transformed to Polygon $Q$ by translation by that directed line segment. Write the number of the corresponding translation in each answer box.

3) Directed line segment $w$.

4) Directed line segment $a$.

5) Directed line segment $v$.

6) Directed line segment $u$.

##### Problem 4

7) Draw the image of quadrilateral $ABCD$ when translated by the directed line segment $v$. Label the image of $A$ as $A'$, the image of $B$ as $B'$, the image of $C$ as $C'$, and the image of $D$ as $D'$.

##### Problem 5

Here is a line $l$.

8) Plot 2 points, $A$ and $B$, which stay in the same place when they are reflected over $l$.

9) Plot 2 other points, $C$ and $D$, which move when they are reflected over $l$.

##### Problem 6

10) Here are 3 points in the plane. Select **all** the straightedge and compass constructions needed to locate the point that is the same distance from all 3 points. Write each corresponding letter in the answer box and separate letters with commas.

a) Construct the bisector of angle $CAB$. $\quad\quad$ b) Construct the bisector of angle $CBA$.

c) Construct the perpendicular bisector of $BC$. $\quad\quad$ d) Construct the perpendicular bisector of $AB$.

e) Construct a line perpendicular to $AB$ through point $C$.$\quad\quad$f) Construct a line perpendicular to $BC$ through point $A$.

##### Problem 7

This straightedge and compass construction shows quadrilateral $ABCD$.

11) Is $ABCD$ a rhombus?

12) Explain how you know.