Lesson 14

Defining Rotations

Problem 1

Draw the image of quadrilateral $$ABCD$$ when rotated $$120^\circ$$ counterclockwise around the point $$D$$.

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Problem 2

There is an equilateral triangle, $$ABC$$, inscribed in a circle with center $$D$$. What is the smallest angle you can rotate triangle $$ABC$$ around $$D$$ so that the image of $$A$$ is $$B$$?

A:

$$60^\circ$$

B:

$$90^\circ$$

C:

$$120^\circ$$

D:

$$180^\circ$$

Problem 3

Which segment is the image of $$AB$$ when rotated $$90^\circ$$ counterclockwise around point $$P$$?

Problem 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.

Solution

(From Unit 1, Lesson 13.)

Problem 5

Here are 2 polygons:

Select all sequences of translations, rotations, and reflections below that would take polygon $$P$$ to polygon $$Q$$.

A:

Rotate $$180^\circ$$ around point $$A$$.

B:

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

C:

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

D:

Reflect over the line $$BA$$ and then rotate $$60^\circ$$ counterclockwise around point $$A$$.

E:

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

Solution

(From Unit 1, Lesson 13.)

Problem 6

1. Draw the image of figure $$ABC$$ when translated by directed line segment $$u$$. Label the image of $$A$$ as $$A’$$, the image of $$B$$ as $$B’$$, and the image of $$C$$ as $$C’$$.
2. Explain why the line containing $$AB$$ is parallel to the line containing $$A’B’$$.

Solution

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 $$D’$$: