Incorporating Rotations

ID: balum-fipoj
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Incorporating Rotations

Classroom:
Due:
Student Name:
Date Submitted:
Problem 1

1) 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) Rotate 60 60^{\circ} counterclockwise around point AA and then reflect over the line FAFA.

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

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

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

A template for answering this question. Ask your instructor for an alternative.
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.

A template for answering this question. Ask your instructor for an alternative.
Problem 3

Match each directed line segment 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.

A template for answering this question. Ask your instructor for an alternative.

3) Directed line segment ww.

4) Directed line segment aa.

5) Directed line segment vv.

6) Directed line segment uu.

Problem 4

7) 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'.

A template for answering this question. Ask your instructor for an alternative.
Problem 5

Here is a line ll.

A template for answering this question. Ask your instructor for an alternative.

8) Plot 2 points, AA and BB, which stay in the same place when they are reflected over ll.

A template for answering this question. Ask your instructor for an alternative.

9) Plot 2 other points, CC and DD, which move when they are reflected over ll.

A template for answering this question. Ask your instructor for an alternative.
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 CABCAB. \quad\quad b) Construct the bisector of angle CBACBA.

c) Construct the perpendicular bisector of BCBC. \quad\quad d) Construct the perpendicular bisector of ABAB.

e) Construct a line perpendicular to ABAB through point CC.\quad\quadf) Construct a line perpendicular to BCBC through point AA.

A template for answering this question. Ask your instructor for an alternative.
Problem 7

This straightedge and compass construction shows quadrilateral ABCDABCD.

A template for answering this question. Ask your instructor for an alternative.

11) Is ABCDABCD a rhombus?

True or false? Write below.

12) Explain how you know.