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).
Understanding reflections on the coordinate plane
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.
A common mistake, and the fix
Changing the wrong coordinate.
Reflecting across the x-axis changes the sign of y: (3, 2) becomes (3, −2). Changing x instead gives (−3, 2), which is the reflection across the y-axis. Ask which axis is the mirror: the coordinate along that axis stays the same.
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.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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