Perpendicular Line Calculator – Guide & Formulas
Calculate the equation of a perpendicular line passing through a specific point. Features negative reciprocal slope derivations.
Determine the equation of a line perpendicular (at a 90-degree angle) to an existing line, passing through a chosen coordinate point (x₁, y₁).
Key Takeaway
Use the free Perpendicular Line Calculator to calculate the equation of a perpendicular line passing through a specific point. features negative reciprocal slope derivations. Get instant results with step-by-step explanations.
How to Use the Perpendicular Line Calculator
- Input the slope-intercept or standard coefficients of the original line.
- Input the coordinates of the target point (x₁, y₁).
- Observe how the slope is transformed into its negative reciprocal and the new equation is derived.
The Formula
Variable Definitions
- m: Original line slope
- m_perp: Perpendicular slope (negative reciprocal of original)
- (x1, y1): Coordinate the perpendicular line must pass through
Orthogonal Structural Line
Find a line perpendicular to y = 2x + 1 that passes through the point (4, 6).
- Step 1: Original slope m = 2.
- Step 2: Calculate perpendicular slope: m_perp = -1 / 2 = -0.5.
- Step 3: Apply point-slope form: y - 6 = -0.5(x - 4).
- Step 4: Expand and simplify: y - 6 = -0.5x + 2 => y = -0.5x + 8.
Frequently Asked Questions
What is a negative reciprocal slope?
It is the negative value of 1 divided by the original slope. For example, if the slope is 3/4, the perpendicular slope is -4/3.
What is the perpendicular slope of a horizontal line?
A horizontal line has slope m = 0. Its perpendicular line is vertical, which has an undefined slope (represented as x = k).
What is the product of perpendicular slopes?
Multiplying two perpendicular slopes (neither of which is vertical/horizontal) always equals exactly -1 (m * m_perp = -1).