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 = 3Output:0.5625Input:a = 4, b = 3, c = 12Output: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

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