How this calculation works
Mirror a point across an arbitrary line in the plane.
THE FORMULA
P′ = P − 2(Ax+By+C)(A,B)/(A²+B²)A worked example
Reflecting (3,4) across y=1 gives (3,−2).
Good to know
The two line coefficients cannot both be zero.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Mirror a point across an arbitrary line in the plane.
The primary result is labeled “Reflected x”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The two line coefficients cannot both be zero.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Reflecting (3,4) across y=1 gives (3,−2).
Which rule does this calculator apply?
P′ = P − 2(Ax+By+C)(A,B)/(A²+B²)