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Point Reflection Calculator

Find the mirror-image coordinates of a point reflected over an axis or the origin.

Result

-3.00
5.00

How it is calculated

You enter the point (x, y) and choose what to reflect it over. The rule only changes signs. Over the x-axis, (x, y) → (x, −y): the point keeps its horizontal position and flips vertically. Over the y-axis, (x, y) → (−x, y). Over the origin, (x, y) → (−x, −y), which is the same as reflecting over both axes, or a 180° rotation about (0, 0). The distance to the axis or origin does not change. Results are rounded to 2 decimals. Only these three mirrors are offered; reflection over a line like y = x or over another point is not covered.

Worked example

Reflect the point (3, −5) over the origin. Both signs flip: the new x is −3 and the new y is −(−5) = 5. The reflected point is (-3.00, 5.00). Over the x-axis the same point would become (3, 5), and over the y-axis it would become (−3, −5). Each answer lies the same distance from the mirror as the original point: the distance to the origin is √(9 + 25) ≈ 5.83 both before and after.

Try this example →

Common mistakes

  • Flipping both signs for an axis reflection. Over the x-axis only y changes sign, and over the y-axis only x does; both flip only for the origin.
  • Mixing up which axis is the mirror. Reflecting over the x-axis changes the y value, which feels backwards but is correct because the mirror line is horizontal.
  • Forgetting that a point on the mirror does not move. (3, 0) reflected over the x-axis stays at (3, 0), because −0 is 0.
  • Entering the point as (y, x). The first field is the horizontal coordinate and the second the vertical one, so check the order.
  • Expecting reflection over y = x or x = 2. Only the two axes and the origin are available; a line elsewhere needs a different formula.

About this calculator

Reflecting a point over the x-axis, y-axis or the origin produces its mirror image: the coordinate on the far side of the axis at the exact same distance, with one or both signs flipped depending on which axis is used. This is one of the four basic rigid transformations in geometry, alongside rotation, translation and glide reflection.

Game developers and graphics programmers use point reflection when mirroring sprites or building symmetric level layouts, and students use it constantly in coordinate geometry to build intuition for how transformations affect a shape's position without changing its size or form. It is also the mathematical basis behind symmetry checks in CAD software.

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