Calculator Inputs
Formula Used
Reflection across the x-axis keeps the horizontal coordinate unchanged and reverses the sign of the vertical coordinate. This makes the reflected point equally far from the x-axis on the opposite side.
Point reflection: (x, y) → (x, -y)
Matrix form: Rx = [[1, 0], [0, -1]]
Vertical change: Δy = y′ - y = -2y
Distance moved: |Δy| = 2|y|
In physics and coordinate analysis, this reflection is useful for symmetry checks, mirror-image path studies, wave diagrams, motion sketches, and geometric transformations.
How to Use This Calculator
- Enter a single X and Y coordinate, or paste multiple points in the batch field.
- Choose the label, unit name, and decimal precision you want in the output.
- Click Calculate Reflection to generate the mirrored coordinates.
- Review the summary cards, detailed result table, and Plotly graph.
- Download the output as CSV or PDF for reports, assignments, or recordkeeping.
Example Data Table
| Example Point | Original Coordinate | Reflected Coordinate | Distance Moved |
|---|---|---|---|
| A | (2, 5) | (2, -5) | 10 |
| B | (-3, 4) | (-3, -4) | 8 |
| C | (6, -2) | (6, 2) | 4 |
| D | (0, 7) | (0, -7) | 14 |
Frequently Asked Questions
1) What does reflecting across the x-axis do?
It keeps the x-value the same and changes the sign of the y-value. A point above the x-axis moves the same distance below it.
2) What is the formula for x-axis reflection?
The standard rule is (x, y) → (x, -y). In matrix form, multiply the coordinate vector by [[1, 0], [0, -1]].
3) Does the distance from the x-axis change?
No. The absolute vertical distance stays the same. Only the side of the axis changes, so the point becomes a mirror image.
4) Can I reflect multiple points together?
Yes. Use the batch field and enter one coordinate pair per line. The calculator processes each point and creates a full result table.
5) Why is the x-value unchanged?
Reflection happens around the horizontal axis only. That flips vertical position, while horizontal placement remains fixed.
6) Is this useful in physics?
Yes. It helps with symmetry models, image methods, mirrored trajectories, coordinate transforms, and wave or motion visualization.
7) What happens if the point lies on the x-axis?
If y = 0, the reflected point is unchanged. Points on the mirror line remain fixed after reflection.
8) What does the distance moved represent?
It is the straight vertical travel from the original point to its reflection. Its value equals 2|y| for each point.