Reflection Transformation Calculator

Work out reflection transformation instantly with clear inputs, formula shown and shareable results.

About Reflection Transformation Calculator

Reflection flips a point across a mirror line. In the x-axis y changes sign, in the y-axis x changes sign, in y = x the coordinates swap, in y = −x they swap and both negate, and through the origin both simply negate.

Formulas

In the x-axis

(x, y) → (x, −y)

In y = x

(x, y) → (y, x)

Through the origin

(x, y) → (−x, −y)

Worked example

With the default values below, Reflection Transformation Calculator returns Image point of (3, -5). Change any input above and every figure here is recalculated in your browser.

Inputs used

Point x: 3
Point y: 5
Reflect inone of x-axis, y-axis, line y = x, line y = −x, the origin: x-axis

Results

Image point: (3, -5)
New x: 3.0000
New y: -5.0000
Distance moved: 10.0000

Step by step

1Values used
2In the x-axis
3In y = x
4Through the origin
5Image point= (3, -5)
6New x= 3.0000
7New y= -5.0000
8Distance moved= 10.0000

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

Reflecting (3, 5) in the x-axis?

It becomes (3, −5), a displacement of 10 units.

Is reflection through the origin the same as a 180° rotation?

Yes, in two dimensions they are identical maps.