Perpendicular Line Calculator

Introduction

Calculating the perpendicular distance between a point and a line is a fundamental operation in geometry. Whether you’re a student studying mathematics or a professional working on spatial problems, having a reliable Perpendicular Line Calculator can save time and ensure accuracy in your calculations. In this article, we’ll provide a user-friendly calculator code along with an explanation of the formula and how to use it.

How to Use

To use the Perpendicular Line Calculator, simply input the coordinates of the point and the equation of the line. Click the “Calculate” button, and the result will be displayed instantly. The calculator employs the precise formula for finding the perpendicular distance between a point and a line, ensuring accurate and reliable results.

Formula

The formula for calculating the perpendicular distance (d) between a point (x₁, y₁) and a line Ax + By + C = 0 is given by:

d=A2+B2​∣Ax1​+By1​+C∣​

Where:

• (x1​,y1​) are the coordinates of the point.
• $A,B,$ and $C$ are the coefficients of the line equation.

Example

Let’s consider a point with coordinates (2, 3) and a line with the equation 2x – 3y + 4 = 0. Using the Perpendicular Line Calculator:

d=22+(−3)2​∣(2×2)+(−3×3)+4∣​

d=4+9​∣4−9+4∣​

d=13​∣−1∣​

d≈13​1​

$d\approx 0.267$

The perpendicular distance is approximately 0.267 units.

FAQs

Q1: Can I use this calculator for 3D coordinates?

A1: No, this calculator is designed for 2D coordinates only. For 3D coordinates, a different formula is required.

Q2: What units should I use for the coordinates?

A2: The units for coordinates should be consistent (e.g., both in meters or both in centimeters).

Q3: Can I use fractions in the line equation?

A3: Yes, the calculator handles fractional coefficients in the line equation.

Conclusion

In conclusion, the Perpendicular Line Calculator presented here provides a quick and accurate way to determine the perpendicular distance between a point and a line in a 2D plane. Whether you’re working on geometry problems or real-world applications, this calculator can be a valuable tool for your calculations.