Perp Line Calculator
Use the Perp Line Calculator for a transparent, instant calculation with validated inputs and cited sources. For a query such as “line perpendicular to line”, enter the matching values and units below and review the stated assumptions.
How to use this calculator
Enter the requested values and units.
Review the assumptions and any warnings shown with the result.
Use the result together with the cited source and your real-world requirements.
Formula
Use the two entered original-line points to form Δx and Δy; the perpendicular slope is −Δx/Δy and its equation passes through the entered target point, with explicit horizontal and vertical cases.
Worked example
Worked example: Inputs: Original line point 1 — x₁: 0; Original line point 1 — y₁: 0; Original line point 2 — x₂: 2; Original line point 2 — y₂: 4; Point the perpendicular line passes through — x: 1; Point the perpendicular line passes through — y: 3. Outputs: Original line slope: 2; Perpendicular slope: -0.5; Perpendicular y-intercept: 3.5; Perpendicular line equation: y - 3 = -0.5(x - 1).
Assumptions and limits
- The result depends on the values, units, and assumptions entered. It does not infer missing context.
Sources
- OpenStax, Rice University: Precalculus 2eReference material reviewed for the stated method, units, or domain. Confirm that its scope matches your use case. Reviewed 2026-08-14.
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Frequently asked questions
How does the Perp Line Calculator work?
Use the two entered original-line points to form Δx and Δy; the perpendicular slope is −Δx/Δy and its equation passes through the entered target point, with explicit horizontal and vertical cases.
What should I enter?
Original line point 1 — x₁, Original line point 1 — y₁, Original line point 2 — x₂, Original line point 2 — y₂, Point the perpendicular line passes through — x, Point the perpendicular line passes through — y
What should I verify?
Review the assumptions and any warnings shown with the result. The result depends on the values, units, and assumptions entered. It does not infer missing context.
Last updated 2026-08-14 · math-perp-line-v1 · opportunity-content-2026-08-14 · Trusty Calculator Editorial Team