Symmetry in the Coordinate Plane Worksheet

Printable “Coordinate Geometry” Worksheets:
Plot Ordered Pairs (First Quadrant)
Symmetry in the Coordinate Planes & Lines
Parallel Lines & Coordinate Plane

Ordered Pairs (Four Quadrants)
Symmetry in the Coordinate Plane
Coordinate Plane (Horizontal & Vertical Distance)

Free printable and online worksheets to help Grade 6 students learn how to recognize that when two ordered pairs differ only by the sign of one or both of the coordinates, then the locations of the points are related by reflections across one or both axes. Reflection of points about the x-axis and the y-axis.

Symmetry in the Coordinate Plane

Reflection Across the x-axis (y = 0):
When a point (x, y) is reflected across the x-axis, its y-coordinate is negated, but the x-coordinate remains the same. The reflected image will be at (x, -y).
Imagine a point plotted at (2, 4). Reflecting it across the x-axis would result in a new point at (2, -4), because the y-coordinate (4) flips to its negative (-4) while the x-coordinate (2) stays the same.

Reflection Across the y-axis (x = 0):
In this reflection, the x-coordinate is negated, and the y-coordinate remains unchanged. The reflected image will be at (-x, y). Consider a point plotted at (3, 1). Reflecting it across the y-axis would result in a new point at (-3, 1), because the x-coordinate (3) flips to its negative (-3) while the y-coordinate (1) stays the same.

Have a look at this video if you need to review how to reflect points about the x-axis and the y-axis.

• Introduction to Symmetry about the x-axis, y-axis, and the origin Using Points

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(Answers on the second page.)
Symmetry in the Coordinate Plane Worksheet #1
Symmetry in the Coordinate Plane Worksheet #2
Symmetry in the Coordinate Plane Worksheet #3

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Symmetry in the Coordinate Plane

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