## Engage NY Eureka Math 8th Grade Module 2 Lesson 3 Answer Key

### Eureka Math Grade 8 Module 2 Lesson 3 Exercise Answer Key

Exercise 1.

Draw a line passing through point P that is parallel to line L. Draw a second line passing through point P that is parallel to line L and that is distinct (i.e., different) from the first one. What do you notice?

Answer:

Students should realize that they can only draw one line through point P that is parallel to L.

Exercises 2–4 (9 minutes)

Students complete Exercises 2–4 independently in preparation for the discussion that follows.

Exercise 2.

Translate line L along the vector \(\overrightarrow{A B}\). What do you notice about L and its image, L’?

Answer:

L and L’ coincide. L=L’.

Exercise 3.

Line L is parallel to vector \(\overrightarrow{A B}\). Translate line L along vector (AB) ⃗. What do you notice about L and its image, L’?

Answer:

L and L’ coincide, again. L=L’.

Exercise 4.

Translate line L along the vector \(\overrightarrow{A B}\). What do you notice about L and its image, L’?

Answer:

L || L’

Exercises 5–6 (5 minutes)

Students complete Exercises 5 and 6 in pairs or small groups.

Exercise 5.

Line L has been translated along vector \(\overrightarrow{A B}\), resulting in L’. What do you know about lines L and L’?

Answer:

L || T(L)

Question 6.

Translate L_{1} and L_{2} along vector \(\overrightarrow{D E}\). Label the images of the lines. If lines L_{1} and L_{2} are parallel, what do you know about their translated images?

Answer:

Since L_{1} || L_{1}, then (L_{1})’ || (L_{2})’.

### Eureka Math Grade 8 Module 2 Lesson 3 Exit Ticket Answer Key

Question 1.

Translate point Z along vector \(\overrightarrow{A B}\). What do you know about the line containing vector \(\overrightarrow{A B}\) and the line formed when you connect Z to its image Z’?

Answer:

The line containing vector \(\overrightarrow{A B}\) and ZZ’ is parallel.

Question 2.

Using the above diagram, what do you know about the lengths of segment ZZ’ and segment AB?

Answer:

The lengths are equal: |ZZ’|=|AB|.

Question 3.

Let points A and B be on line L and the vector \(\overrightarrow{A C}\) be given, as shown below. Translate line L along vector \(\overrightarrow{A C}\). What do you know about line L and its image, L’? How many other lines can you draw through point C that have the same relationship as L and L’? How do you know?

Answer:

L and L’ are parallel. There is only one line parallel to line L that goes through point C. The fact that there is only one line through a point parallel to a given line guarantees it.

### Eureka Math Grade 8 Module 2 Lesson 3 Problem Set Answer Key

Question 1.

Translate ∠XYZ, point A, point B, and rectangle HIJK along vector \(\overrightarrow{E F}\). Sketch the images, and label all points using prime notation.

Answer:

Question 2.

What is the measure of the translated image of ∠XYZ? How do you know?

Answer:

The measure is 38°. Translations preserve angle measure.

Question 3.

Connect B to B’. What do you know about the line that contains the segment formed by BB’ and the line containing the vector \(\overrightarrow{E F}\)?

Answer:

\(\overleftrightarrow{\boldsymbol{B B}^{\prime}} \| \overleftrightarrow{\boldsymbol{E F}}\)

Question 4.

Connect A to A’. What do you know about the line that contains the segment formed by AA’ and the line containing the vector \(\overrightarrow{\boldsymbol{E F}}\)?

Answer:

\(\overleftrightarrow{A A^{\prime}}\) and \(\overleftrightarrow{\boldsymbol{E F}}\) coincide.

Question 5.

Given that figure HIJK is a rectangle, what do you know about lines that contain segments HI and JK and their translated images? Explain.

Answer:

Since HIJK is a rectangle, I know that \(\overleftrightarrow{\boldsymbol{H} \boldsymbol{I}}\) || \(\overleftrightarrow{\boldsymbol{J K}}\). Since translations map parallel lines to parallel lines, then \(\overleftrightarrow{\boldsymbol{H}^{\prime} \boldsymbol{I}^{\prime}}\)||\(\overleftrightarrow{\boldsymbol{J}^{\prime} \boldsymbol{K}^{\prime}}\).