# Perpendicular Line Calculator

## About Perpendicular Line Calculator (Formula)

A Perpendicular Line Calculator is a tool used in geometry to determine the equation of a line that is perpendicular to a given line. Perpendicular lines have slopes that are negative reciprocals of each other. This calculator helps find the equation of a line that passes through a given point and is perpendicular to a specified line. The formula used to calculate the equation of a perpendicular line involves the slope and the point-slope form of a linear equation.

The formula for calculating the equation of a perpendicular line passing through a point (x₁, y₁) and perpendicular to a line with slope m is:

Equation of Perpendicular Line: y – y₁ = (-1/m) * (x – x₁)

Where:

• Equation of Perpendicular Line is the equation of the line that is perpendicular to the given line and passes through the specified point.
• (x₁, y₁) is the coordinates of the given point through which the perpendicular line passes.
• m is the slope of the given line.

Using the Perpendicular Line Calculator involves these steps:

1. Input: Enter the coordinates of the point (x₁, y₁) and the slope of the given line into the calculator.
2. Calculation: The calculator applies the formula to calculate the equation of the perpendicular line.
3. Output: The calculator displays the equation of the perpendicular line.

This tool is particularly useful for geometry students, mathematicians, and engineers who work with lines and angles and need to find equations of perpendicular lines for various applications.

For example, if you have a line with a slope of 2 and you want to find the equation of a line perpendicular to it that passes through the point (3, 4), the Perpendicular Line Calculator will provide you with the equation of the perpendicular line.

In geometry and mathematics, perpendicular lines play a fundamental role in understanding angles, shapes, and spatial relationships.