Reflection Calculator
Reflect a point across the x-axis, y-axis, origin, or the line y=x.
About Reflection Calculator
Reflection maps a point to its mirror image across a line or point. Standard reflections: x-axis flips y, y-axis flips x, origin flips both, y=x swaps coordinates.
Formulas
Reflection across x-axis
(x, y) → (x, −y)
- x
- Original x
- y
- Original y
Reflection across y-axis
(x, y) → (−x, y)
- x
- Original x
- y
- Original y
Reflection across y=x
(x, y) → (y, x)
- x
- Original x
- y
- Original y
Worked example
With the default values below, Reflection Calculator returns Image X of 3.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Point x
- 3
- Point y
- 5
- Reflect Acrossone of x-axis, y-axis, Origin, Line y = x, Line y = -x
- x-axis
Results
- Image X
- 3.0000
- Image Y
- -5.0000
Step by step
- 1Rule applied= Reflect across x-axis: (x, y) → (x, −y)
- 2Image point
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Can I reflect across an arbitrary line?
This calculator handles the five standard reflection axes. For an arbitrary line, use the general reflection formula involving the perpendicular foot.
Is reflection a rigid transformation?
Yes — it preserves distances and angles but reverses orientation (like a mirror).