Lesson 13

Incorporating Rotations

The practice problem answers are available at one of our IM Certified Partners

Problem 1

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:

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

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 the directed line segment with the image of Polygon $$P$$ being transformed to Polygon $$Q$$ by translation by that directed line segment.

(From Geometry, Unit 1, Lesson 12.)

Problem 4

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 $$D’$$.

(From Geometry, Unit 1, Lesson 12.)

Problem 5

Here is a line $$\ell$$

Plot 2 points, $$A$$ and $$B$$, which stay in the same place when they are reflected over $$\ell$$. Plot 2 other points, $$C$$ and $$D$$, which move when they are reflected over $$\ell$$

(From Geometry, Unit 1, Lesson 11.)

Problem 6

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.

A:

Construct the bisector of angle $CAB$.

B:

Construct the bisector of angle $CBA$.

C:

Construct the perpendicular bisector of $BC$.

D:

Construct the perpendicular bisector of $AB$.

E:

Construct a line perpendicular to $AB$ through point $C$.

F:

Construct a line perpendicular to $BC$ through point $A$.

(From Geometry, Unit 1, Lesson 9.)

Problem 7

This straightedge and compass construction shows quadrilateral $$ABCD$$. Is $$ABCD$$ a rhombus? Explain how you know.

(From Geometry, Unit 1, Lesson 7.)