Reflections Across the Axes (Grades 6–8)
A reflection flips a point across an axis like a mirror. Reflecting across the x-axis keeps x the same and flips the sign of y: (3, 2) → (3, −2). Reflecting across the y-axis keeps y the same and flips the sign of x: (3, 2) → (−3, 2). The point lands the same distance from the axis, on the opposite side.
Understanding reflections on the coordinate plane
A reflection flips a point across an axis like a mirror. Reflecting across the x-axis keeps x the same and flips the sign of y: (3, 2) → (3, −2). Reflecting across the y-axis keeps y the same and flips the sign of x: (3, 2) → (−3, 2). The point lands the same distance from the axis, on the opposite side.
Key Idea
A reflection flips a point across an axis like a mirror. Reflecting across the x-axis keeps x the same and flips the sign of y: (3, 2) → (3, −2). Reflecting across the y-axis keeps y the same and flips the sign of x: (3, 2) → (−3, 2). The point lands the same distance from the axis, on the opposite side.
Seeing it in action
Worked example
Reflect (3, 2) across the x-axis.
Keep x = 3, flip y: 2 → −2. → (3, −2).
Across the x-axis, x stays and y changes sign.
Try a few
Reflect (4, 5) across the y-axis
Reflect (−2, 3) across the x-axis
Reflect (1, −6) across the x-axis
Coordinate Quest
A calm treasure-map game for plotting, reading, and translating points on a coordinate plane.
Ready for the interactive lab?
Practice reflections on the coordinate plane in Numeris with instant feedback.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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