Check whether two straight lines are orthogonal or not

23 Jun, 2022
Given two line segments AB and CD having A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4). The task is to check whether these two lines are orthogonal or not. Two lines are called orthogonal if they are perpendicular at the point of intersection. 
Examples:  
Input: x1 = 0, y1 = 3, x2 = 0, y2 = -5
        x3 = 2, y3 = 0, x4 = -1, y4 = 0
Output: Yes

Input:  x1 = 0, y1 = 4, x2 = 0, y2 = -9
        x3 = 2, y3 = 0, x4 = -1, y4 = 0
Output: Yes
 
Approach: If the slopes of the two lines are m1 and m2 then for them to be orthogonal we need to check if:  
Both lines have infinite slope then answer is no.
One line has infinite slope and if other line has 0 slope then answer is yes otherwise no.
Both lines have finite slope and their product is -1 then the answer is yes.
Below is the implementation of the above approach: 
C++
Java
Python3
C#
PHP
Javascript
// C++ implementation of above approach#include <bits/stdc++.h>using namespace std; // Function to check if two straight// lines are orthogonal or notbool checkOrtho(int x1, int y1, int x2, int y2,                int x3, int y3, int x4, int y4){     int m1, m2;     // Both lines have infinite slope    if (x2 - x1 == 0 && x4 - x3 == 0)        return false;     // Only line 1 has infinite slope    else if (x2 - x1 == 0) {         m2 = (y4 - y3) / (x4 - x3);         if (m2 == 0)            return true;        else            return false;    }     // Only line 2 has infinite slope    else if (x4 - x3 == 0) {         m1 = (y2 - y1) / (x2 - x1);         if (m1 == 0)            return true;        else            return false;    }     else {        // Find slopes of the lines        m1 = (y2 - y1) / (x2 - x1);        m2 = (y4 - y3) / (x4 - x3);         // Check if their product is -1        if (m1 * m2 == -1)            return true;        else            return false;    }} // Driver codeint main(){    int x1 = 0, y1 = 4, x2 = 0, y2 = -9;    int x3 = 2, y3 = 0, x4 = -1, y4 = 0;     checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4) ? cout << "Yes"                                               : cout << "No";     return 0;}
//Java implementation of above approach import java.io.*; class GFG {         // Function to check if two straight    // lines are orthogonal or not    static boolean checkOrtho(int x1, int y1, int x2, int y2,                    int x3, int y3, int x4, int y4)    {         int m1, m2;             // Both lines have infinite slope        if (x2 - x1 == 0 && x4 - x3 == 0)            return false;         // Only line 1 has infinite slope        else if (x2 - x1 == 0)        {            m2 = (y4 - y3) / (x4 - x3);            if (m2 == 0)                return true;            else                return false;        }         // Only line 2 has infinite slope        else if (x4 - x3 == 0)        {             m1 = (y2 - y1) / (x2 - x1);            if (m1 == 0)                return true;            else                return false;        }         else        {            // Find slopes of the lines            m1 = (y2 - y1) / (x2 - x1);            m2 = (y4 - y3) / (x4 - x3);             // Check if their product is -1            if (m1 * m2 == -1)                return true;            else                return false;        }    }     // Driver code    public static void main (String[] args)    {        int x1 = 0, y1 = 4, x2 = 0, y2 = -9;        int x3 = 2, y3 = 0, x4 = -1, y4 = 0;         if(checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4)==true)            System.out.println ("Yes");        else            System.out.println("No" );    }} //This code is contributed by akt_mit..
# Python 3 implementation of above approach # Function to check if two straight# lines are orthogonal or notdef checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4):         # Both lines have infinite slope    if (x2 - x1 == 0 and x4 - x3 == 0):        return False     # Only line 1 has infinite slope    elif (x2 - x1 == 0):        m2 = (y4 - y3) / (x4 - x3)         if (m2 == 0):            return True        else:            return False     # Only line 2 has infinite slope    elif (x4 - x3 == 0):        m1 = (y2 - y1) / (x2 - x1);         if (m1 == 0):            return True        else:            return False     else:                 # Find slopes of the lines        m1 = (y2 - y1) / (x2 - x1)        m2 = (y4 - y3) / (x4 - x3)         # Check if their product is -1        if (m1 * m2 == -1):            return True        else:            return False     # Driver codeif __name__ == '__main__':    x1 = 0    y1 = 4    x2 = 0    y2 = -9    x3 = 2    y3 = 0    x4 = -1    y4 = 0         if(checkOrtho(x1, y1, x2, y2,                  x3, y3, x4, y4)):        print("Yes")    else:        print("No") # This code is contributed by# Shashank_Sharma
// C# implementation of above approachusing System; class GFG{         // Function to check if two straight    // lines are orthogonal or not    static bool checkOrtho(int x1, int y1, int x2, int y2,                    int x3, int y3, int x4, int y4)    {         int m1, m2;             // Both lines have infinite slope        if (x2 - x1 == 0 && x4 - x3 == 0)            return false;         // Only line 1 has infinite slope        else if (x2 - x1 == 0)        {            m2 = (y4 - y3) / (x4 - x3);            if (m2 == 0)                return true;            else                return false;        }         // Only line 2 has infinite slope        else if (x4 - x3 == 0)        {            m1 = (y2 - y1) / (x2 - x1);            if (m1 == 0)                return true;            else                return false;        }         else        {            // Find slopes of the lines            m1 = (y2 - y1) / (x2 - x1);            m2 = (y4 - y3) / (x4 - x3);             // Check if their product is -1            if (m1 * m2 == -1)                return true;            else                return false;        }    }     // Driver code    public static void Main ()    {        int x1 = 0, y1 = 4, x2 = 0, y2 = -9;        int x3 = 2, y3 = 0, x4 = -1, y4 = 0;         if(checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4) == true)            Console.WriteLine("Yes");        else            Console.WriteLine("No" );    }} // This code is contributed by Ryuga
<?php// PHP implementation of above approach // Function to check if two straight// lines are orthogonal or notfunction checkOrtho($x1, $y1, $x2, $y2,                    $x3, $y3, $x4, $y4){     // Both lines have infinite slope    if ($x2 - $x1 == 0 && $x4 - $x3 == 0)        return false;     // Only line 1 has infinite slope    else if ($x2 - $x1 == 0)    {        $m2 = (int)(($y4 - $y3) / ($x4 - $x3));         if ($m2 == 0)            return true;        else            return false;    }     // Only line 2 has infinite slope    else if ($x4 - $x3 == 0)    {        $m1 = (int)(($y2 - $y1) / ($x2 - $x1));         if ($m1 == 0)            return true;        else            return false;    }     else    {                 // Find slopes of the lines        $m1 = (int)(($y2 - $y1) / ($x2 - $x1));        $m2 = (int)(($y4 - $y3) / ($x4 - $x3));         // Check if their product is -1        if ($m1 * $m2 == -1)            return true;        else            return false;    }} // Driver code$x1 = 0; $y1 = 4;$x2 = 0; $y2 = -9;$x3 = 2; $y3 = 0;$x4 = -1; $y4 = 0; if(checkOrtho($x1, $y1, $x2, $y2,              $x3, $y3, $x4, $y4))    print("Yes");else    print("No"); // This code is contributed by chandan_jnu?>
<script>    // Javascript implementation of above approach         // Function to check if two straight    // lines are orthogonal or not    function checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4)    {           let m1, m2;               // Both lines have infinite slope        if (x2 - x1 == 0 && x4 - x3 == 0)            return false;           // Only line 1 has infinite slope        else if (x2 - x1 == 0)        {            m2 = parseInt((y4 - y3) / (x4 - x3), 10);            if (m2 == 0)                return true;            else                return false;        }           // Only line 2 has infinite slope        else if (x4 - x3 == 0)        {            m1 = parseInt((y2 - y1) / (x2 - x1), 10);            if (m1 == 0)                return true;            else                return false;        }           else        {            // Find slopes of the lines            m1 = parseInt((y2 - y1) / (x2 - x1), 10);            m2 = parseInt((y4 - y3) / (x4 - x3), 10);               // Check if their product is -1            if (m1 * m2 == -1)                return true;            else                return false;        }    }         let x1 = 0, y1 = 4, x2 = 0, y2 = -9;    let x3 = 2, y3 = 0, x4 = -1, y4 = 0;     if(checkOrtho(x1, y1, x2, y2, x3, y3, x4, y4) == true)      document.write("Yes");    else      document.write("No" ); </script>
Yes
 
Time Complexity: O(1)
Auxiliary Space: O(1)
jit_t
Shashank_Sharma
ankthon
Chandan_Kumar
divyeshrabadiya07
sushmitamittal1329
Geometric-Lines
Geometric
Mathematical
Mathematical
Geometric
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