# Lesson 12

Defining Translations

### Problem 1

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

### Problem 2

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 3

Which statement is true about a translation?

A:

A translation takes a line to a parallel line or itself.

B:

A translation takes a line to a perpendicular line.

C:

A translation requires a center of translation.

D:

A translation requires a line of translation.

### Problem 4

Select all the points that stay in the same location after being reflected across line $$\ell$$

A:

A

B:

B

C:

C

D:

D

E:

E

### Solution

(From Unit 1, Lesson 11.)

### Problem 5

Lines $$\ell$$ and $$m$$ are perpendicular. A point $$Q$$ has this property: rotating $$Q$$ 180 degrees using center $$P$$ has the same effect as reflecting $$Q$$ over line $$m$$

1. Give two possible locations of $$Q$$.
2. Do all points in the plane have this property?

### Solution

(From Unit 1, Lesson 11.)

### Problem 6

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 $$D’$$:

### Solution

(From Unit 1, Lesson 10.)

### Problem 7

Two distinct lines, $$\ell$$ and $$m$$, are each perpendicular to the same line $$n$$

1. What is the measure of the angle where line $$\ell$$ meets line $$n$$?
2. What is the measure of the angle where line $$m$$ meets line $$n$$?