# Defining Translations

ID: fuzir-lanaj Illustrative Math
Subject: Geometry

# Defining Translations

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##### 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?

a) $\text{A translation takes a line to a parallel line or itself. }$b) $\text{A translation takes a line to a perpendicular line. }$c) $\text{A translation requires a center of translation. }$d) $\text{A translation requires a line of translation.}$
##### 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?

True or false? Write below.
##### 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 ﻿$n$﻿?