Area of triangle formed by the axes of co-ordinates and a given straight line

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++

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// 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;
}

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Java

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// 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.

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Python3

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# 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

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C#

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// 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. 

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PHP

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<?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
?>

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Output:

0.5625


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