# Perpendicular Line Calculator

Finding the **equation** of lines is one of the most common calculations in **vector** Mathematics. Being a student, you must have been **asked** to find the equation of a perpendicular line using another line’s equation or coordinates. If you don’t know how to do this with **accuracy**, you should use this **Perpendicular Line Calculator**.

It is a free online maths calculator that can quickly find such an **equation**. This online calculator has been programmed for this purpose that **adopts** your given input values and uses them to find a **line** that will be perpendicular to the line you have inserted. If you want to know more about this **tool** and this specific type of line, read on till the **end**.

**Table of Contents**

## Perpendicular Line Definition

A perpendicular line is a specific **term** used for those lines that intersect another line or **set** of lines at an **angle** of 90 degrees. In simple **words**, a line that will **cut** another line vertically straight will be called a **perpendicular line**.

It is **not** compulsory that a line has only **one ** line of this type. We can **draw** as many perpendicular lines as we need on a single line because we can draw a line making **90 degrees** of angle on different points of the same line. In **Mathematics**, a perpendicular line is shown by inserting “**⫡**” this symbol between the lines. **For example**, if the AB line is perpendicular to the CD line, it will be written as “**AB ⫡ CD**”.

### Formula for a Perpendicular Line

There is no quick **formula** that we can write here in a **single** line. We have to derive its formula **step** by step to understand how you can **calculate** the perpendicular line.

Let us have a line with the following equation,

y = ax + b

Now, we have to find the perpendicular line. Let’s assume the line has coordinates x0 and y0. So, we can write the equation of the new line (Perpendicular line) as,

^{y}0 = mx^{0}+ r

As we know that the product of the slopes of two perpendicular lines is equal to -1. So,

a * m = -1 r

It can also be written as,

a = -1/m

So, the equation of the perpendicular line will become,

^{y}0 = -1/m *^{x}0 + b

^{y}0 = -^{x}0/m + b

We can also rewrite the equation to find the value of b and complete the equation of a perpendicular line.

## How to find the Perpendicular Line?

**No doubt**, it is a difficult task to find the equation of a perpendicular line. But we have **solved** an example here to let you understand it **properly**.

**Example 1:**

Find the equation of a line that passes through (4, 8) and is perpendicular to y = 4x + 6.

**Solution:**

By comparing the given equations with the above formulas, we know,

m = 4 and r = 6

Now, we have to find the values for “a” and “b” using the above equations/formulas.

a = -1/m

a = -¼

a = -0.25

The equation of the new line can be written as,

y = -0.25x + b

Using the values of a point from which this line must pass,

8 = -0.25 (4) + b

8 = -1 + b

b = 9

So, the final equation of the perpendicular line will be written as,

y = -0.25x +9

### How to use a perpendicular line calculator?

It may be **hard** for you to find the equation or follow the above **steps**. You can use this online tool Calculator’s Bag by following these simple steps.

- Insert the values related to the given line i.e. slope and value of “r”.
- Write the coordinates of the point from which the line must pass
- This calculator will show the line that will be perpendicular to the given line and pass through the point.

### FAQ | Perpendicular Line Calculator

**Are perpendicular lines always 90?**

Yes, perpendicular lines must make an angle of 90 degrees to the line on which these are drawn.

**Do perpendicular lines add up to 180?**

A perpendicular line makes an angle of 90 degrees with another line. It is not a closed shape that will add up its angles to make 180 degrees.

**What are perpendicular lines?**

All lines that are drawn on other lines by making an angle of 90 degrees are called perpendicular lines.

**Why is the product of slopes of two perpendicular lines equal to -1? **

It is a rule of vector Mathematics that the slope of two perpendicular lines is equal to -1 because these are fully opposite to each other. .

**Can perpendicular lines be noncoplanar? **

Yes, Perpendicular lines can be noncoplanar.