# Incorporating Rotations

ID: balum-fipoj Illustrative Math
Subject: Geometry

# Incorporating Rotations

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##### Problem 1

1) Below are 2 polygons:

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

a) Rotate ﻿$180^{\circ}$﻿ around point ﻿$A$﻿.

b) Rotate ﻿$60^{\circ}$﻿ counterclockwise around point ﻿$A$﻿ and then reflect over the line ﻿$FA$﻿.

c) Translate so that ﻿$A$﻿ is taken to ﻿$J$﻿. Then reflect over line ﻿$BA$﻿.

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

e) Reflect over the line ﻿$BA$﻿ and then rotate ﻿$60^{\circ}$﻿ counterclockwise around point ﻿$A$﻿. ##### 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. ##### Problem 3

Match each directed line segment 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. 3) Directed line segment ﻿$w$﻿.

4) Directed line segment ﻿$a$﻿.

5) Directed line segment ﻿$v$﻿.

6) Directed line segment ﻿$u$﻿.

##### Problem 4

7) 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 5

Here is a line ﻿$l$﻿. 8) Plot 2 points, ﻿$A$﻿ and ﻿$B$﻿, which stay in the same place when they are reflected over ﻿$l$﻿. 9) Plot 2 other points, ﻿$C$﻿ and ﻿$D$﻿, which move when they are reflected over ﻿$l$﻿. ##### 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 ﻿$CAB$﻿. ﻿$\quad\quad$﻿ b) Construct the bisector of angle ﻿$CBA$﻿.

c) Construct the perpendicular bisector of ﻿$BC$﻿. ﻿$\quad\quad$﻿ d) Construct the perpendicular bisector of ﻿$AB$﻿.

e) Construct a line perpendicular to ﻿$AB$﻿ through point ﻿$C$﻿.﻿$\quad\quad$﻿f) Construct a line perpendicular to ﻿$BC$﻿ through point ﻿$A$﻿. ##### Problem 7

This straightedge and compass construction shows quadrilateral ﻿$ABCD$﻿. 11) Is ﻿$ABCD$﻿ a rhombus?

True or false? Write below.

12) Explain how you know.