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Area of triangle formed by the axes of co-ordinates and a given straight line
  • Last Updated : 18 Mar, 2021

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
 

  1. Let PQ be the straight line having AB, the line segment between the axes. 
    The equation is, 
    ax + by + c = 0 
     
  2. so, in intercept form it can be expressed as, 
    x/(-c/a) + y/(-c/b) = 1 
     
  3. So, the x-intercept = -c/a 
    the y-intercept = -c/b 
     
  4. 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 
     
  5. So, area of the triangle 
    AOB =|c^2/(2*a*b)|
     

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

 

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