# Symmetry in the Coordinate Plane

Videos to help Grade 6 students understand symmetry in the coordinate plane.

New York State Common Core Math Grade 6, Module 3, Lesson 16

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### New York State Common Core Math Module 3, Grade 6, Lessons 16

Lesson 15 Review

4. Locate and label at least five points on the coordinate plane that have an x-coordinate of 6.
a. What is true of the y-coordinates below the x-axis?
b. What is true of the y-coordinates above the x-axis?
c. What must be true of the y-coordinates on the x-axis?

Lesson 16 Student Outcomes

Students understand that two numbers are said to differ only by signs if they are opposite of each other.

Students recognize that when two ordered pairs differ only by sign of one or both of the coordinates, then the locations of the points are related by reflections across one or both axes.

Example 1: Extending Opposite Numbers to the Coordinate Plane

Locate and label the points (3, 4) and (-3, 4)

Locate and label your points on the coordinate plane. 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.

Lesson 16 Exercise

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.
a. When the coordinates of two points are (x, y) and (-x, y) what line of symmetry do the points share? Explain.
b. When the coordinates of two points are (x, y) and (x, -y) what line of symmetry do the points share? Explain.
To reflect over x-axis the x-coordinate stays the same and the y-coordinate is opposite.
To reflect over y-axis the y-coordinate stays the same and the x-coordinate is opposite.

Lesson 16 Exit Ticket

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?

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. Problem Set
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. 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. 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?

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

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