# Perpendicular line

This tool calculates the equation of a perpendicular line to a given line (of equation y = mx + p), passing through a point of coordinates (a,b).

## How to calculate the perpendicular line to a given line, passing through a point ?

(See representation above)

Given a line D of equation (y = m * x + p), we want to calculate the equation of the line E that is perpendicular to D and passing through a given point M of coordinates (a,b).

We denote :

M : point of coordonates (a , b)

D : line of equation y = mx + p

E : perpendicular line to D passing through point M.

E equation is y = nx + q. We search for n and q values.

Formulas are the following :

n = -1/m , because the product of two perpendicular lines slopes (m and n in this case) is equal to -1.

q = b - na, since E passes through M.

## See also

Line Calculator

Coordinate Geometry calculators

Geometry calculators

Mathematics calculators