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

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 <bits/stdc++.h>
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

<script>
    // Javascript 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 
    function pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2) 
    { 
        let fx1; // Variable to store a * x1 + b * y1 - c 
        let 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; 
    } 
    
    let a = 1, b = 1, c = 1; 
    let x1 = 1, y1 = 1; 
    let x2 = 2, y2 = 1; 
  
    if (pointsAreOnSameSideOfLine(a, b, c, x1, y1, x2, y2)) 
        document.write("Yes"); 
    else
        document.write("No"); 

// This code is contributed by divyesh072019.
</script>

Output:

Yes

Time complexity: O(1) because constant operations are done

Auxiliary space: O(1)

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