Math
Distance from point to line
Measure the shortest perpendicular distance from a point to the infinite straight line defined by A×x + B×y + C = 0.
Calculators / Math / Point reflected across a line
Point reflected across a line calculator
Reflect a point across a line written as ax + by + c = 0.
On this page
Reflected x-3
Reflected y4
Calculator controls
How to calculate
Reflect a point across a line written as ax + by + c = 0.
Reflected x =
x-a*(2*(a*x+b*y+c)/(a^2+b^2))Reflected y =
y-b*(2*(a*x+b*y+c)/(a^2+b^2))Worked example
- Point x: 3
- Point y: 4
- Line x coefficient: 1
- Line y coefficient: 0
- Line constant: 0
- Reflected x: -3
- Reflected y: 4
Assumptions and limits
Line coefficients a and b cannot both be zero. Use an orthonormal Cartesian coordinate system; nonuniform map scales do not preserve this reflection.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Reflect a point across a line written as ax + by + c = 0. The original and reflected points are equally distant from the line on opposite sides.
When this tool is useful
The original and reflected points are equally distant from the line on opposite sides.
Understanding your inputs
| Input | Example |
|---|---|
Point x x | 3 |
Point y y | 4 |
Line x coefficient a | 1 |
Line y coefficient b | 0 |
Line constant c | 0 |
Frequently asked questions
Which assumptions matter for this result?
Line coefficients a and b cannot both be zero. Use an orthonormal Cartesian coordinate system; nonuniform map scales do not preserve this reflection.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.