Given a straight line with equation coefficients as a, b & c(ax + by + c = 0), the task is to find the area of the triangle formed by the axes of co-ordinates and this straight line.
Examples:
Input: a = -2, b = 4, c = 3 Output: 0.5625 Input: a = 4, b = 3, c = 12 Output: 6
Approach:
- Let PQ be the straight line having AB, the line segment between the axes.
The equation is,
ax + by + c = 0
- so, in intercept form it can be expressed as,
x/(-c/a) + y/(-c/b) = 1
- So, the x-intercept = -c/a
the y-intercept = -c/b
- So, it is very clear now the base of the triangle AOB will be -c/a
and the base of the triangle AOB will be -c/b
- So, area of the triangle
Below is the implementation of the above approach:
C++
// C++ program area of triangle // formed by the axes of co-ordinates // and a given straight line #include <bits/stdc++.h> using namespace std;
// Function to find area double area( double a, double b, double c)
{ double d = fabs ((c * c) / (2 * a * b));
return d;
} // Driver code int main()
{ double a = -2, b = 4, c = 3;
cout << area(a, b, c);
return 0;
} |
Java
// Java program area of triangle // formed by the axes of co-ordinates // and a given straight line import java.io.*;
class GFG
{ // Function to find area static double area( double a, double b, double c)
{ double d = Math.abs((c * c) / ( 2 * a * b));
return d;
} // Driver code public static void main (String[] args)
{ double a = - 2 , b = 4 , c = 3 ;
System.out.println(area(a, b, c));
} } // This code is contributed by ajit. |
Python3
# Python3 program area of triangle # formed by the axes of co-ordinates # and a given straight line # Function to find area def area(a, b, c):
d = abs ((c * c) / ( 2 * a * b))
return d
# Driver code a = - 2
b = 4
c = 3
print (area(a, b, c))
# This code is contributed # by mohit kumar |
C#
// C# program area of triangle // formed by the axes of co-ordinates // and a given straight line using System;
class GFG
{ // Function to find area static double area( double a, double b, double c)
{ double d = Math.Abs((c * c) / (2 * a * b));
return d;
} // Driver code static public void Main ()
{ double a = -2, b = 4, c = 3;
Console.WriteLine (area(a, b, c));
} } // This code is contributed by akt_mit. |
PHP
<?php // PHP program area of triangle // formed by the axes of co-ordinates // and a given straight line // Function to find area function area( $a , $b , $c )
{ $d = abs (( $c * $c ) / (2 * $a * $b ));
return $d ;
} // Driver code $a = -2;
$b = 4;
$c = 3;
echo area( $a , $b , $c );
// This code is contributed by Ryuga ?> |
Javascript
<script> // javascript program area of triangle // formed by the axes of co-ordinates // and a given straight line // Function to find area function area(a , b , c)
{ var d = Math.abs((c * c) / (2 * a * b));
return d;
} // Driver code var a = -2, b = 4, c = 3;
document.write(area(a, b, c)); // This code is contributed by Amit Katiyar </script> |
Output:
0.5625
Time Complexity: O(1)
Auxiliary Space: O(1)