How to use this calculator

A reflection puts a point the same perpendicular distance on the opposite side of a mirror line. It preserves lengths and angles while reversing orientation. Enter one point or several vertices to compare the original and reflected coordinates in a table and plot.

The method

t = (ax + by + c)/(a^2 + b^2); reflected point = (x - 2at, y - 2bt)

Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.

WORKED EXAMPLE

Points to reflect: 3,4; -2,1 Reflect across: x-axis (y = 0)

Reflected coordinates: 2 points reflected

Across the selected line in the coordinate plane.

Scope and limitations

Up to 100 points. A custom line needs at least one nonzero coefficient among a and b. Graphs use equal coordinate scales; points on the line remain fixed.

Common questions

What happens to a point on the mirror line?

It stays where it is because its perpendicular distance from the line is zero.

What line coefficients should I use for y = 2x + 1?

Rewrite it as 2x - y + 1 = 0, then enter a = 2, b = -1, c = 1.

References & further reading

External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.