Reflection Calculator
Reflect a point across the x-axis, y-axis, origin, or the line y=x.
Inputs
Image X
3.0000
Image Y
-5.0000
Step by step
Rule applied
= Reflect across x-axis: (x, y) → (x, −y)
Image point
(3, 5) → (3, -5)
How it works
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
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).