## Introduction to Perpendicular Line Calculator:

Perpendicular line Calculator is a tool designed that is used to **find the equation of a line** from the perpendicular line that passes through a specific point. The calculator is a valuable tool in geometry as it provides a way to determine and simplify the process of finding perpendicular lines.

The perpendicular slope calculator is a useful tool for students, professionals, and anyone who is working with geometry problems and is not familiar with perpendicular concepts, it gives you a complete procedure while you use it for finding different examples.

## What is a Perpendicular Line?

A perpendicular line is a line that makes a **90-degree angle** with another line in geometry and it can be expressed with ⊥ a symbol. When two lines m1 and m2 are perpendicular, they intersect each other and form a right angle. The slopes of perpendicular lines are the negative reciprocals of the equation of a line or a point.

Perpendicular lines are fundamental elements that play a crucial role in various mathematical and practical applications. As it provides a basis for understanding angles, shapes, and spatial relationships between them.

## What is the Rule for Perpendicular Lines?

There are two distinct lines l and q in a plane, it makes a right angle (90c) when they intersect. The slope of perpendicular lines l and q are the **negative reciprocal** of the given equation. The perpendicular line calculator uses the following perpendicular slope formula for evaluation,

$$ y \;=\; mx + c $$

$$ml\; mq \;=\; -1 $$

$$ m_l \;=\; -\frac{1}{m_q} $$

$$ m_q \;=\; -\frac{1}{m_l} $$

## How to Solve Perpendicular Line?

To **find the slope** of a perpendicular line, the perpendicular line equation calculator finds out the slope of the equation of a line and the point at which a line passes through it. Let's see how to solve the perpendicular line from the given equation.

**Method 1**: Use the Slope and a Point,

- If the slope of the original line is given in question then, let us suppose the slope of the line is m1.
- To find m2 you need to take the negative reciprocal of m1 as:

$$ m_2 \;=\; \frac{−1}{m_1} $$

- If you have a point is a perpendicular line that passes through it, denote the coordinates as (
**x1,y1**)

$$ y - y_1 \;=\; m(x - x_1) $$

where m is the slope

**Method 2**: Use the Equations of Lines

- If the equation of the line, let us the
**y=mx + b**, where m is the slope and b is the y-intercept. - To find the slope of the perpendicular line from m1, the m2 is the negative reciprocal of m1.
- If you have a specific point, you can choose any point on the original line. Then use the point-slope that forms with the slope of 𝑚2.

$$ m_2 \;=\; \frac{-1}{m_1} $$

- If you have the equation of the original line, you can use its slope directly to find the slope of the perpendicular line.

The perpendicular equation calculator uses both methods to solve the perpendicular line according to the given questions.

## Solved Example of a Perpendicular Line:

Let's observe an **example** that explains the calculation process of the perpendicular line Calculator and find out how to calculate perpendicular line problems manually. For that, the examples are given below,

**Example**:

The line l passes through points (0,1) and (1,3) and the line q passes through points (-1, 4) then Find out if the given lines are perpendicular.

**Solution**:

To find the perpendicular line first find the slope of the equation

$$ ml \;=\; \frac{y_2 - y_1}{x_2 - x_1} $$

$$ mq \;=\; \frac{y_2 - y_1}{x_2 - x_1} $$

$$ ml \;=\; \frac{3 - 1}{1 - 0} $$

$$ =\; \frac{2}{1} \;=\; 2 $$

The slope of line q, mq passes through the points (-1, 4) and (5,1) is,

$$ m_q \;=\; \frac{1 - 4}{5 - (-1)} $$

$$ =\; \frac{-3}{6} $$

$$ =\; \frac{-1}{2} $$

Now lines l and q are perpendicular if and only if,

$$ m_l \;=\; -\frac{1}{m_q} \;and\; m_q \;=\; -\frac{1}{m_l} $$

$$ m_l \;=\; 2 \;and\; m_q \;=\; -\frac{1}{m_l} \;=\; -\frac{1}{2} $$

As, the slopes of the lines are negative reciprocals so that lines l and q are perpendicular lines.

## How to Use Perpendicular Line Calculator?

The perpendicular slope calculator has a simple layout that enables you to calculate the perpendicular line from the given equation. Follow our guidelines before using it to find the solution to the equation and get an amazing experience. These guidelines are:

- Enter the equation in the form of “y=mx+c” to find the perpendicular line in the input field of the perpendicular equation calculator.
- Review your equation before pressing the calculate button of the perpendicular line equation calculator to get the precise solution without any mistakes.
- Click on the “
**Calculate**” button to get the solution of the perpendicular line problem. - Click on the “Recalculate” button to get a new page for more evaluation of the perpendicular line questions.
- If you want to check the accuracy of our perpendicular lines calculator then you should first try out the load example and get an accurate solution every time.

## Final Result of Perpendicular Slope Calculator:

The calculator for perpendicular lines gives you a solution to your given orthogonal equation problem after you click on the calculated button. It may include the following:

**Result Option**:

The result option provides you with **solutions** for Perpendicular line problems.

**Possible Steps**:

Possible steps of perpendicular lines calculator provide you with solutions to Perpendicular line equation examples in a step-wise process.

## Benefits of Using Perpendicular Line Equation Calculator:

The calculator for perpendicular lines provides you many benefits whenever you use it to calculate the equation question to find its solution. These benefits help you to get a better understanding of Perpendicular line concepts.

- The perpendicular gradient calculator
**saves the time**and energy that you consume for finding the orthogonal equation questions manually. - It is a handy tool, so you can easily use it to solve the orthogonal equation
- The line perpendicular calculator has a user-friendly design so that you can solve different equations easily.
- The perpendicular slope calculator provides you with an accurate solution as per your given input term for the perpendicular line question
- Perpendicular line Calculator is an educational tool that helps you to become familiar with the concept of the perpendicular line through an online platform.