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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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Lesson Plans and Worksheets for Grade 6

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More Lessons for Grade 6

Common Core For Grade 6

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.




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