Perpendicular Line Calculator

Math

Perpendicular Line Calculator finds the equation of a line perpendicular to a given line and passing through a point. Perpendicular slope = -1/m (negative reciprocal).

Formula

m_perp = -1/m; y - y₀ = m_perp(x - x₀)
  • Perpendicular slopes are negative reciprocals
  • Passes through given point (x₀, y₀)

Example

Inputs
  • Original Line Slope (m): 2
  • Point X-coordinate (x₀): 3
  • Point Y-coordinate (y₀): 4

Slope 2 → perpendicular -0.5 through (3,4)

Frequently asked questions

What is a perpendicular line?
A line intersecting at 90° with slope = -1/original_slope
Why negative reciprocal?
Product of perpendicular slopes = -1 (from dot product)