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# Check whether two points (x1, y1) and (x2, y2) lie on same side of a given line or not

• Difficulty Level : Basic
• Last Updated : 19 Mar, 2021

Given three integers a, b and c which represents coefficients of the equation of a line a * x + b * y – c = 0. Given two integer points (x1, y1) and (x2, y2). The task is to determine whether the points (x1, y1) and (x2, y2) lie on the same side of the given line or not.
Examples:

Input : a = 1, b = 1, c = 1, x1 = 1, y1 = 1, x2 = 1, y2 = 2
Output : yes
On applying (x1, y1) and (x2, y2) on a * x + b * y – c, gives 1 and 2 respectively both of which have the same sign, hence both the points lie on same side of the line.
Input : a = 1, b = 1, c = 1, x1 = 1, y1 = 1, x2 = 0, y2 = 0
Output : no

Approach : Apply both the points on given line equation and check if the obtained values belong to same parity or not.
Below is the implementation of the above approach:

## C++

 `// C++ program to check if two points``// lie on the same side or not``#include ``using` `namespace` `std;` `// Function to check if two points``// lie on the same side or not``bool` `pointsAreOnSameSideOfLine(``int` `a, ``int` `b, ``int` `c,``                        ``int` `x1,    ``int` `y1, ``int` `x2, ``int` `y2)``{``    ``int` `fx1; ``// Variable to store a * x1 + b * y1 - c``    ``int` `fx2; ``// Variable to store a * x2 + b * y2 - c` `    ``fx1 = a * x1 + b * y1 - c;``    ``fx2 = a * x2 + b * y2 - c;` `    ``// If fx1 and fx2 have same sign``    ``if` `((fx1 * fx2) > 0)``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``int` `main()``{``    ``int` `a = 1, b = 1, c = 1;``    ``int` `x1 = 1, y1 = 1;``    ``int` `x2 = 2, y2 = 1;` `    ``if` `(pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;``}`

## Java

 `// Java program to check if two points``// lie on the same side or not``import` `java.util.*;` `class` `GFG``{` `// Function to check if two points``// lie on the same side or not``static` `boolean` `pointsAreOnSameSideOfLine(``int` `a, ``int` `b,``                                         ``int` `c, ``int` `x1,``                                         ``int` `y1, ``int` `x2,``                                         ``int` `y2)``{``    ``int` `fx1; ``// Variable to store a * x1 + b * y1 - c``    ``int` `fx2; ``// Variable to store a * x2 + b * y2 - c` `    ``fx1 = a * x1 + b * y1 - c;``    ``fx2 = a * x2 + b * y2 - c;` `    ``// If fx1 and fx2 have same sign``    ``if` `((fx1 * fx2) > ``0``)``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `a = ``1``, b = ``1``, c = ``1``;``    ``int` `x1 = ``1``, y1 = ``1``;``    ``int` `x2 = ``2``, y2 = ``1``;` `    ``if` `(pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2))``        ``System.out.println(``"Yes"``);``    ``else``        ``System.out.println(``"No"``);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to check if two points``# lie on the same side or not` `# Function to check if two points``# lie on the same side or not``def` `pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2):``    ``fx1 ``=` `0` `# Variable to store a * x1 + b * y1 - c``    ``fx2 ``=` `0` `# Variable to store a * x2 + b * y2 - c` `    ``fx1 ``=` `a ``*` `x1 ``+` `b ``*` `y1 ``-` `c``    ``fx2 ``=` `a ``*` `x2 ``+` `b ``*` `y2 ``-` `c` `    ``# If fx1 and fx2 have same sign``    ``if` `((fx1 ``*` `fx2) > ``0``):``        ``return` `True` `    ``return` `False` `# Driver code``a, b, c ``=` `1``, ``1``, ``1``x1, y1 ``=` `1``, ``1``x2, y2 ``=` `2``, ``1` `if` `(pointsAreOnSameSideOfLine(a, b, c,``                              ``x1, y1, x2, y2)):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)` `# This code is contributed by Mohit Kumar`

## C#

 `// C# program to check if two points``// lie on the same side or not``using` `System;``class` `GFG``{` `// Function to check if two points``// lie on the same side or not``static` `bool` `pointsAreOnSameSideOfLine(``int` `a, ``int` `b,``                                      ``int` `c, ``int` `x1,``                                      ``int` `y1, ``int` `x2,``                                      ``int` `y2)``{``    ``int` `fx1; ``// Variable to store a * x1 + b * y1 - c``    ``int` `fx2; ``// Variable to store a * x2 + b * y2 - c` `    ``fx1 = a * x1 + b * y1 - c;``    ``fx2 = a * x2 + b * y2 - c;` `    ``// If fx1 and fx2 have same sign``    ``if` `((fx1 * fx2) > 0)``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `a = 1, b = 1, c = 1;``    ``int` `x1 = 1, y1 = 1;``    ``int` `x2 = 2, y2 = 1;` `    ``if` `(pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2))``        ``Console.WriteLine(``"Yes"``);``    ``else``        ``Console.WriteLine(``"No"``);``}``}` `// This code is contributed by Code_Mech`

## Javascript

 ``
Output:
`Yes`

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