Perpendicular Line Calculator

Summary

Enter a line (y = mx + b or two points) and a point — get the equation of the perpendicular line through that point instantly.

How it works

1. Choose whether to define the original line using slope-intercept form (y = mx + b) or by two points.
2. Enter the required values for the original line.
3. Enter the coordinates of the point the perpendicular line must pass through.
4. Click "Calculate" — the tool computes the negative reciprocal of the slope.
5. The perpendicular line equation is shown in both slope-intercept and standard form.
6. Edge cases: a horizontal original line produces a vertical perpendicular, and vice versa.

Use cases

• Geometry homework — find the line perpendicular to a given line at a specific point.
• Verify textbook answers for perpendicular line problems.
• Computer graphics — calculate normals to line segments.
• Engineering drawings that require right-angle constructions.
• Analytic geometry — check if two lines are perpendicular (slopes are negative reciprocals).
• Build altitude lines in triangle geometry problems.

Frequently Asked Questions