# 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.

### Solution

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### 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 \(D’\).

### Solution

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### Problem 3

Which statement is true about a translation?

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

A translation takes a line to a perpendicular line.

A translation requires a center of translation.

A translation requires a line of translation.

### Solution

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### Problem 4

Select **all** the points that stay in the same location after being reflected across line \(\ell\).

A

B

C

D

E

### Solution

### 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 \(m\).

- Give two possible locations of \(Q\).
- Do all points in the plane have this property?

### Solution

### 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

### Problem 7

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

- What is the measure of the angle where line \(\ell\) meets line \(n\)?
- What is the measure of the angle where line \(m\) meets line \(n\)?