Defining Rotations

ID: jovik-nunod
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Defining Rotations

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Problem 1

1) Draw the image of quadrilateral ABCDABCD when rotated 120120^{\circ} counterclockwise around the point DD.

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Problem 2

2) There is an equilateral triangle,ABCABC, inscribed in a circle with center DD. What is the smallest angle you can rotate triangle ABCABC around DD so that the image of AA is BB?

a) 60  60^{\circ} \text{ }b) 90  90^{\circ} \text{ }c) 120  120^{\circ} \text{ }d) 180 180^{\circ}
Problem 3

3) Which segment is the image of ABAB when rotated 9090^{\circ} counterclockwise around point PP?

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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.

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Problem 5

5) Below are 2 polygons.

Select all sequences of translations, rotations, and reflections below that would take polygon PP to polygon QQ. Write each corresponding letter in the answer box and separate letters with commas.

a) Rotate 180180^{\circ} around point AA.

b) Translate so that AA is taken to JJ. Then reflect over line BABA.

c) Rotate 6060^{\circ} counterclockwise around point AA and then reflect over the line FAFA.

d) Reflect over the line BABA and then rotate 6060^{\circ} counterclockwise around point AA.

e) Reflect over line BABA and then translate by directed line segment BABA.

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Problem 6

6) Draw the image of figure ABCABC when translated by directed line segment uu. Label the image of AA as AA', the image of BB as BB', and the image of CC as CC'.

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7) Explain why the line containing ABAB is parallel to the line containing ABA'B'.

Problem 7

8) 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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