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 areadouble area(double a, double b, double c){ double d = fabs((c * c) / (2 * a * b)); return d;}// Driver codeint 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 lineimport java.io.*;class GFG{// Function to find areastatic double area(double a, double b, double c){ double d = Math.abs((c * c) / (2 * a * b)); return d;}// Driver codepublic 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 areadef area(a, b, c): d = abs((c * c) / (2 * a * b)) return d# Driver codea = -2b = 4c = 3print(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 lineusing System;class GFG{ // Function to find areastatic double area(double a, double b, double c){ double d = Math.Abs((c * c) / (2 * a * b)); return d;}// Driver codestatic 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 areafunction 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)
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