# Find a Perpendicular Line Through a Point - Calculator

A calculator to find the equation of a line that is perpendicular to a given line and passing through a point.

## Equation of a Line Perpendicular to Another Line and Through a point P

The slope $ m $ of line L given by the equation $A x + B y = C$ is given by$m = - \dfrac{A}{B}$

If two lines are perpendicular, the product of their slopes is equal to -1. Hence the slope of the line perpendicular to line L is given by

$ m' = - 1 /( - \dfrac{A}{B}) = \dfrac{B}{A}$

The equation, in point slope form, of a line parallel to line L and through point P (a,b) is given by

$y - b = \dfrac{B}{A} (x - a)$

## How to use the calculator

1 - Enter the coordinates of the point through which the line passes.2 - Enter A, B and C the coefficients of the the given line defined as follows.

$ A x + B y = C $ 3 - press "enter". The answer is an equation, in slope intercept form, of the line perpendicular to the line entered and passing through the point entered .

The coordinates and coefficients may be entered as fractions, integers or decimals.(see examples below).