# Length of the normal from origin on a straight line whose intercepts are given

Given the intercepts of a straight line on both the axes as **m** and **n**. The task is to find the length of the normal on this straight line from the origin.

**Examples:**

Input:m = 5, n = 3

Output:2.57248

Input:m = 13, n = 9

Output:7.39973

**Approach:** A normal to a line is a line segment drawn from a point perpendicular to the given line.

Let **p** be the length of the normal drawn from the origin to a line, which subtends an angle **Θ** with the positive direction of x-axis as follows.

Then, we have **cos Θ = p / m** and **sin Θ = p / n**

Since, **sin ^{2} Θ + cos^{2} Θ = 1**

So,

**(p / m)**

^{2}+ (p / n)^{2}= 1We get,

**p = m * n / √(m**

^{2}+ n^{2})Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the normal ` `// of the straight line ` `float` `normal(` `float` `m, ` `float` `n) ` `{ ` ` ` `// Length of the normal ` ` ` `float` `N = (fabsf(m) * fabsf(n)) ` ` ` `/ ` `sqrt` `((fabsf(m) * fabsf(m)) ` ` ` `+ (fabsf(n) * fabsf(n))); ` ` ` ` ` `return` `N; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `m = -5, n = 3; ` ` ` `cout << normal(m, n); ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java implementation of the approach ` `class` `GFG ` `{ ` ` ` `// Function to find the normal ` `// of the straight line ` `static` `float` `normal(` `float` `m, ` `float` `n) ` `{ ` ` ` `// Length of the normal ` ` ` `float` `N = (` `float` `) ((Math.abs(m) * Math.abs(n)) ` ` ` `/ Math.sqrt((Math.abs(m) * Math.abs(m)) ` ` ` `+ (Math.abs(n) * Math.abs(n)))); ` ` ` ` ` `return` `N; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `float` `m = -` `5` `, n = ` `3` `; ` ` ` `System.out.println(normal(m, n)); ` `} ` `} ` ` ` `// This code has been contributed by 29AjayKumar ` |

*chevron_right*

*filter_none*

## Python3

# Python3 implementation of the approach

import math;

# Function to find the normal

# of the straight line

def normal(m, n):

# Length of the normal

N = ((abs(m) * abs(n)) /

math.sqrt((abs(m) * abs(m)) +

(abs(n) * abs(n))));

return N;

# Driver code

m = -5; n = 3;

print(normal(m, n));

# This code is contributed

# by Akanksha Rai

## C#

`// C# implementation of the approach ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the normal ` `// of the straight line ` `static` `float` `normal(` `float` `m, ` `float` `n) ` `{ ` ` ` `// Length of the normal ` ` ` `float` `N = (` `float` `)((Math.Abs(m) * Math.Abs(n)) / ` ` ` `Math.Sqrt((Math.Abs(m) * Math.Abs(m)) + ` ` ` `(Math.Abs(n) * Math.Abs(n)))); ` ` ` ` ` `return` `N; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `float` `m = -5, n = 3; ` ` ` `Console.Write(normal(m, n)); ` `} ` `} ` ` ` `// This code is contributed by Akanksha Rai ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP implementation of the approach ` ` ` `// Function to find the normal ` `// of the straight line ` `function` `normal(` `$m` `, ` `$n` `) ` `{ ` ` ` `// Length of the normal ` ` ` `$N` `= (` `abs` `(` `$m` `) * ` `abs` `(` `$n` `)) / ` ` ` `sqrt((` `abs` `(` `$m` `) * ` `abs` `(` `$m` `)) + ` ` ` `(` `abs` `(` `$n` `) * ` `abs` `(` `$n` `))); ` ` ` ` ` `return` `$N` `; ` `} ` ` ` `// Driver code ` `$m` `= -5; ` `$n` `= 3; ` `echo` `normal(` `$m` `, ` `$n` `); ` ` ` `// This code is contributed by Ryuga ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

2.57248

## Recommended Posts:

- Equation of straight line passing through a given point which bisects it into two equal line segments
- Represent a given set of points by the best possible straight line
- Check if a line passes through the origin
- Check if it is possible to draw a straight line with the given direction cosines
- Area of triangle formed by the axes of co-ordinates and a given straight line
- Number of jump required of given length to reach a point of form (d, 0) from origin in 2D plane
- Klee's Algorithm (Length Of Union Of Segments of a line)
- Length of the perpendicular bisector of the line joining the centers of two circles
- Check whether two straight lines are orthogonal or not
- Check if given two straight lines are identical or not
- Check if three straight lines are concurrent or not
- Find K Closest Points to the Origin
- Lexicographically Kth smallest way to reach given coordinate from origin
- Count of different straight lines with total n points with m collinear
- Find normal at a given point on the curve

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.