# Distance between two parallel lines

Given are two parallel straight lines with slope **m**, and different y-intercepts **b1** & **b2**.The task is to find the distance between these two parallel lines.

**Examples:**

Input:m = 2, b1 = 4, b2 = 3Output:0.333333Input:m = -4, b1 = 11, b2 = 23Output:0.8

- Let
**PQ**and**RS**be the parallel lines, with equations

**y = mx + b1**

y = mx + b2 - The distance between these two lines is the distance between the two intersection points of these lines with the perpendicular line.Let that distance be
**d**. - So, equation of the line perpendicular to
**PQ**and**RS**can be

**y = -x/m** - Now, solving the perpendicular line with PQ and RS separately to get the intersecting points
**(x1, y1)**&**(x2, y2)**, we get, - From
**PQ**,

**y = mx + b1**

y = -x/m

(x1, y1) = ( -b1*m/(m^2 + 1), b1/(m^2 + 1)) - From
**RS**,

**y = mx + b2**

y = -x/m

(x2, y2) = ( -b2*m/(m^2 + 1), b2/(m^2 + 1)) - So,
**d = distance between (x1, y1) and (x2, y2)**

**Below is the implementation of the above approach**:

## C++

`// C++ program find the distance ` `// between two parallel lines ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the distance ` `// between parallel lines ` `double` `dist(` `double` `m, ` `double` `b1, ` `double` `b2) ` `{ ` ` ` `double` `d = ` `fabs` `(b2 - b1) / ((m * m) - 1); ` ` ` `return` `d; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `double` `m = 2, b1 = 4, b2 = 3; ` ` ` `cout << dist(m, b1, b2); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java program find the distance ` `// between two parallel lines ` `class` `GFG ` `{ ` ` ` `// Function to find the distance ` `// between parallel lines ` `static` `double` `dist(` `double` `m, ` ` ` `double` `b1, ` `double` `b2) ` `{ ` ` ` `double` `d = Math.abs(b2 - b1) / ` ` ` `((m * m) - ` `1` `); ` ` ` `return` `d; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `double` `m = ` `2` `, b1 = ` `4` `, b2 = ` `3` `; ` ` ` `System.out.println(dist(m, b1, b2)); ` `} ` `} ` ` ` `// This code is contributed by Code_Mech. ` |

*chevron_right*

*filter_none*

## Python3

`# Python3 program find the distance ` `# between two parallel lines ` ` ` `# Function to find the distance ` `# between parallel lines ` `def` `dist(m, b1, b2): ` ` ` `d ` `=` `abs` `(b2 ` `-` `b1) ` `/` `((m ` `*` `m) ` `-` `1` `); ` ` ` `return` `d; ` ` ` `# Driver Code ` `def` `main(): ` ` ` `m, b1, b2 ` `=` `2` `,` `4` `, ` `3` `; ` ` ` `print` `(dist(m, b1, b2)); ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` `main() ` ` ` `# This code contributed by PrinciRaj1992 ` |

*chevron_right*

*filter_none*

## C#

`// C# program find the distance ` `// between two parallel lines ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the distance ` `// between parallel lines ` `static` `double` `dist(` `double` `m, ` ` ` `double` `b1, ` `double` `b2) ` `{ ` ` ` `double` `d = Math.Abs(b2 - b1) / ` ` ` `((m * m) - 1); ` ` ` `return` `d; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main() ` `{ ` ` ` `double` `m = 2, b1 = 4, b2 = 3; ` ` ` `Console.Write(dist(m, b1, b2)); ` `} ` `} ` ` ` `// This code is contributed by Akanksha Rai ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program find the distance ` `// between two parallel lines ` ` ` `// Function to find the distance ` `// between parallel lines ` `function` `dist(` `$m` `, ` `$b1` `, ` `$b2` `) ` `{ ` ` ` `$d` `= ` `abs` `(` `$b2` `- ` `$b1` `) / ((` `$m` `* ` `$m` `) - 1); ` ` ` `return` `$d` `; ` `} ` ` ` `// Driver Code ` `$m` `= 2; ` `$b1` `= 4; ` `$b2` `= 3; ` ` ` `echo` `dist(` `$m` `, ` `$b1` `, ` `$b2` `); ` ` ` `// This code is contributed by Ryuga ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

0.333333

## Recommended Posts:

- Find whether only two parallel lines contain all coordinates points or not
- Maximum number of region in which N non-parallel lines can divide a plane
- Number of parallelograms when n horizontal parallel lines intersect m vertical parallellines
- Distance between two parallel Planes in 3-D
- Count paths with distance equal to Manhattan distance
- Find Four points such that they form a square whose sides are parallel to x and y axes
- Minimum lines to cover all points
- 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
- Maximum points of intersection n lines
- Program for Point of Intersection of Two Lines
- Number of triangles formed from a set of points on three lines
- Non-crossing lines to connect points in a circle
- Pizza cut problem (Or Circle Division by Lines)

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.