## Engage NY Eureka Math 6th Grade Module 3 Lesson 16 Answer Key

### Eureka Math Grade 6 Module 3 Lesson 16 Example Answer Key

Example 1.
Extending Opposite Numbers to the Coordinate Plane
Extending Opposite Numbers to the Coordinates of Points on the Coordinate Plane Locate and label your points on the coordinate plane to the right. For each given pair of points in the table below, record your observations and conjectures in the appropriate cell. Pay attention to the absolute values of the coordinates and where the points lie in reference to each axis.    Examples 2 – 3: Navigating the Coordinate Plane ### Eureka Math Grade 6 Module 3 Lesson 16 Exercise Answer Key

Exercises

In each column, write the coordinates of the points that are related to the given point by the criteria listed in the first column of the table. Point S(5, 3) has been reflected over the x- and y-axes for you as a guide, and its images are shown on the coordinate plane. Use the coordinate grid to help you locate each point and its corresponding coordinates.   Exercise 1.
When the coordinates of two points are (x, y) and (- x, y), what line of symmetry do the points share? Explain.
They share the y-axis because the y-coordinates are the same and the x-coordinates are opposites, which means the points will be the same distance from the y-axis but on opposite sides.

Exercise 2.
When the coordinates of two points are (x, y) and (x, – y). what line of symmetry do the points share? Explain.
They share the x-axis because the x-coordinates are the same and the y-coordinates are opposites, which means the points will be the same distance from the x-axis but on opposite sides.

### Eureka Math Grade 6 Module 3 Lesson 16 Problem Set Answer Key

Question 1.
Locate a point In Quadrant IV of the coordinate plane. Label the point A, and write its ordered pair next to it.

a. Reflect point A over an axis so that its image is in Quadrant III. Label the image B, and write its ordered pair next to it. Which axis did you reflect over? What is the only difference in the ordered pairs of points A and B?
B(- 5, – 3); reflected over the y-axis
The ordered pairs differ only by the sign of their x-coordinates: A(5, – 3) and B(- 5, – 3).

b. Reflect point B over an axis so that its image is in Quadrant II. Label the image C, and write its ordered pair next to it. Which axis did you reflect over? What is the only difference in the ordered pairs of points B and C? How does the ordered pair of point C relate to the ordered pair of point A?
C(- 5, 3); reflected over the x-axis
The ordered pairs differ only by the signs of their y-coordinates: B(- 5, – 3) and C(- 5, 3).
The ordered pair for point C differs from the ordered pair for point A by the signs of both coordinates:
A(5, – 3) and C(- 5, 3).

c. Reflect point C over an axis so that its image is in Quadrant I. Label the image D, and write its ordered pair next to it. Which axis did you reflect over? How does the ordered pair for point D compare to the ordered pair for point C? How does the ordered pair for point D compare to points A and B?
D(5, 3); reflected over the y-axis again
Point D differs from point C by only the sign of its x-coordinate: D(5, 3) and C(- 5, 3).
Point D differs from point B by the signs of both coordinates: D(5, 3) and B(- 5, – 3).
Point D differs from point A by only the sign of the y-coordinate: D(5, 3) and A(5, – 3).

Question 2.
Bobbie listened to her teacher’s directions and navigated from the point (- 1,0) to (5, – 3). She knows that she has the correct answer, but she forgot part of the teacher’s directions. Her teacher’s directions included the following:
“Move 7 units down, reflect about the   ?   -axis, move up 4 units, and then move right 4 units.”
Help Bobbie determine the missing axis in the directions, and explain your answer.
The missing line is a reflection over the y-axis. The first line would move the location to (- 1, – 7). A reflection over the y-axis would move the location to (1, – 7) in Quadrant IV, which is 4 units left and 4 units down from the end point (5, – 3).

### Eureka Math Grade 6 Module 3 Lesson 16 Exit Ticket Answer Key

Question 1.
How are the ordered pairs (4, 9) and (4, – 9) similar, and how are they different? Are the two points related by a reflection over an axis in the coordinate plane? If so, indicate which axis is the line of symmetry between the points. If they are not related by a reflection over an axis in the coordinate plane, explain how you know.
The x-coordinates are the same, but the y-coordinates are opposites, meaning they are the same distance from zero on the x-axis and the same distance but on opposite sides of zero on the y-axis. Reflecting about the x-axis interchanges these two points.

Question 2.
Given the point (- 5, 2), write the coordinates of a point that is related by a reflection over the x- or y-axis. Specify which axis is the line of symmetry.