Find the other end point of a line with given one end and mid using C++

In this problem, we are given the coordinates of two points of a line starting point A(x_A, y_A) and midpoint M(x_M, y_M) .Our task is to find the other end point of a line with given one end and mid.

Let’s take an example to understand the problem,

Input

A = [1, 2], M = [3, 0]

Output

[5, -2]

Explanation

The line is −

Solution Approach

To solve the problem, we will be using the concepts of geometry we have learned in mathematics. If you remember there is a midpoint formula for every line which is,

mid(x) = (x1 + x2) / 2
mid(y) = (y1 + y2) / 2

But we are given the value of the midpoint in the problem and need the value for x2 and y2. So, we will change the formula accordingly.

x2 = 2*mid(x) - x1
y2 = 2*mid(y) - y1

Using the above formula, we can find the value of the other endpoint using the midpoint and one point of the line.

Example

Program to illustrate the working of our solution

#include <iostream>
using namespace std;
void findMissingPointLine(float x1, float y1, float xm, float ym){
   float x2 = (2 * xm) - x1;
   float y2 = (2 * ym) - y1;
   cout<<"B(x, y) = "<<"( "<<x2<<", "<<y2<<" )";
}
int main()
{
   float x1 = -4, y1 = -1, xm = 3, ym = 5;
   cout<<"The other end point of the line is \n";
   findMissingPointLine(x1, y1, xm, ym);
   return 0;
}

Output

The other end point of the line is
B(x, y) = ( 10, 11 )