# Defining Translations

# Defining Translations

##### Problem 1

Match each of the directed line segments 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.

1) Directed line segment $u$.

2) Directed line segment $w$.

3) Directed line segment $a$.

4) Directed line segment $v$.

##### Problem 2

5) 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 3

6) Which statement is true about a translation?

##### Problem 4

7) Select **all** the points that stay in the same location after being reflected across line $l$. Write each corresponding letter in the answer box and separate letters with commas.

a) A $\quad\quad$ b) B $\quad\quad$ c) C $\quad\quad$ d) D $\quad\quad$ e) E

##### Problem 5

Lines $l$ and $m$ are perpendicular. A point $Q$ has this property: rotating $Q$ 180 degrees using center $P$ has the same effect as reflecting $Q$ over line $m$.

8) Give two possible locations of $Q$.

9) Do all points in the plane have this property?

##### Problem 6

10) 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 $D'$:

##### Problem 7

Two distinct lines, $l$ and $m$, are each perpendicular to the same line $n$.

11) What is the measure of the angle where line $l$ meets line $n$?

12) What is the measure of the angle where line $m$ meets line $n$?