Equation of straight line passing through a given point which bisects it into two equal line segments

Given a straight line which passes through a given point (x0, y0) such that this point bisects the line segment in two equal line segments. The task is to find the equation of this straight line.

Examples:

Input: x0 = 4, y0 = 3
Output: 3x + 4y = 24

Input: x0 = 7, y0 = 12
Output: 12x + 7y = 168



Approach:

Let PQ be the line and AB be the line segment between the axes. The x-intercept and y-intercept are a & b respectively.
Now, as C(x0, y0) bisects AB so,
x0 = (a + 0) / 2 i.e. a = 2x0
Similiarly, y0 = (0 + b) / 2 i.e. b = 2y0
We know that the equation of a straight line in intecept form is,

x / a + y / b = 1
Here, a = 2x0 & b = 2y0
So, x / 2x0 + y / 2y0 = 1
or, x / x0 + y / y0 = 2
Therefore, x * y0 + y * x0 = 2 * x0 * y0

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <iostream>
using namespace std;
  
// Function to print the equation
// of the required line
void line(double x0, double y0)
{
    double c = 2 * y0 * x0;
    cout << y0 << "x"
         << " + " << x0 << "y = " << c;
}
  
// Driver code
int main()
{
    double x0 = 4, y0 = 3;
    line(x0, y0);
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG
{
      
// Function to print the equation
// of the required line
static void line(double x0, double y0)
{
    double c = (int)(2 * y0 * x0);
    System.out.println(y0 + "x" + " + "
                       x0 + "y = " + c);
}
  
// Driver code
public static void main(String[] args)
{
    double x0 = 4, y0 = 3;
    line(x0, y0);
}
}
  
// This code is contributed 
// by Code_Mech

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Python3

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# Python 3 implementation of the approach
  
# Function to print the equation
# of the required line
def line(x0, y0):
    c = 2 * y0 * x0
    print(y0, "x", "+", x0, "y=", c)
  
# Driver code
if __name__ == '__main__':
    x0 = 4
    y0 = 3
    line(x0, y0)
      
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# implementation of the approach
using System;
  
class GFG
{
      
// Function to print the equation
// of the required line
static void line(double x0, double y0)
{
    double c = (int)(2 * y0 * x0);
    Console.WriteLine(y0 + "x" + " + "
                    x0 + "y = " + c);
}
  
// Driver code
public static void Main(String[] args)
{
    double x0 = 4, y0 = 3;
    line(x0, y0);
}
}
  
/* This code contributed by PrinciRaj1992 */

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PHP

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<?php
// PHP implementation of the approach 
  
// Function to print the equation 
// of the required line 
function line($x0, $y0
    $c = 2 * $y0 * $x0
    echo $y0 , "x"," + ",
         $x0 , "y = " , $c
  
// Driver code 
$x0 = 4; $y0 = 3; 
line($x0, $y0); 
  
// This code is contributed by Ryuga
?>

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Output:

3x + 4y = 24


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