Defining Translations

ID: fuzir-lanaj
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Defining Translations

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Problem 1

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

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1) Directed line segment uu.

2) Directed line segment ww.

3) Directed line segment aa.

4) Directed line segment vv.

Problem 2

5) Draw the image of quadrilateral ABCDABCD when translated by the directed line segment vv. Label the image of AA as AA', the image of BB as BB', the image of CC as CC' and the image of DD as DD'.

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Problem 3

6) Which statement is true about a translation?

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

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Problem 5

Lines ll and mm are perpendicular. A point QQ has this property: rotating QQ 180 degrees using center PP has the same effect as reflecting QQ over line mm.

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8) Give two possible locations of QQ.

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 AA to AA', BB to BB', and CC to CC'. The same sequence takes DD to DD'. Draw and label DD':

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Problem 7

Two distinct lines, ll and mm, are each perpendicular to the same line nn.

11) What is the measure of the angle where line ll meets line nn?

12) What is the measure of the angle where line mm meets line nn?