Check whether two straight lines are orthogonal or not
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++
// C++ implementation of above approach #include <bits/stdc++.h> using namespace std; // Function to check if two straight // lines are orthogonal or not 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 int 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
//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.. |
Python3
# Python 3 implementation of above approach # Function to check if two straight # lines are orthogonal or not def 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 code if __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#
// C# implementation of above approach using 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 // PHP 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 ) { // 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 ?> |
Javascript
<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> |
Output:
Yes
Time Complexity: O(1)
Auxiliary Space: O(1)