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Find coordinates of the triangle given midpoint of each side

  • Last Updated : 20 Aug, 2021

Given three coordinates (x, y), which are the midpoint of the sides of the triangle. The task is to find the coordinates of the triangle. 

Examples:  

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Input : midx1 = 5, midy1 = 3
        midx2 = 4, midy2 = 4
        midx3 = 5, midy3 = 5

Output : x1 = 4 y1 = 2
         x2 = 4 y2 = 6
         x3 = 6 y3 = 4

Solution can be verified by the figure.

Let’s separately solve for X-coordinates and Y-coordinates. For X coordinate of vertices, let them be x1, x2, x3. Then, X-coordinate of middle points will be (x1 + x2)/2, (x2 + x3)/2, (x3 + x1)/2. Observe, sum of these 3 expressions is equal to sum of X-coordinates. Now, we have sum of 3 variables and 3 expressions for sum of every pair of them, find out the values of coordinates by solving equations. 
Similarly, we solve for Y-coordinates.



Below is the implementation of this approach:  

C++




// C++ program to find coordinate of the
// triangle given midpoint of each side
#include<bits/stdc++.h>
#define N 3
using namespace std;
 
// Return after solving the equations and
// finding the vertices coordinate.
vector<int> solve(int v[])
{
    vector<int> res;
 
    // Finding sum of all three coordinate.
    int all3 = v[0] + v[1] + v[2];
 
    // Solving the equation.
    res.push_back(all3 - v[1]*2);
    res.push_back(all3 - v[2]*2);
    res.push_back(all3 - v[0]*2);
 
    return res;
}
 
// Finds vertices of a triangles from given
// middle vertices.
void findVertex(int xmid[], int ymid[])
{
    // Find X coordinates of vertices.
    vector<int> V1 = solve(xmid);
 
    // Find Y coordinates of vertices.
    vector<int> V2 = solve(ymid);
 
    // Output the solution.
    for (int i = 0; i < 3; i++)
        cout << V1[i] << " "
             << V2[i] <<endl;
}
 
// Driver code
int main()
{
    int xmid[N] = { 5, 4, 5 };
    int ymid[N] = { 3, 4, 5 };
    findVertex(xmid, ymid);
    return 0;
}

Java




import java.util.Vector;
 
// Java program to find coordinate of the
// triangle given midpoint of each side
class GFG {
 
//static final int N = 3;
// Return after solving the equations and
// finding the vertices coordinate.
    static Vector<Integer> solve(int v[]) {
        Vector<Integer> res = new Vector<Integer>();
 
        // Finding sum of all three coordinate.
        int all3 = v[0] + v[1] + v[2];
 
        // Solving the equation.
        res.add(all3 - v[1] * 2);
        res.add(all3 - v[2] * 2);
        res.add(all3 - v[0] * 2);
 
        return res;
    }
 
// Finds vertices of a triangles from given
// middle vertices.
    static void findVertex(int xmid[], int ymid[]) {
        // Find X coordinates of vertices.
        Vector<Integer> V1 = solve(xmid);
 
        // Find Y coordinates of vertices.
        Vector<Integer> V2 = solve(ymid);
 
        // Output the solution.
        for (int i = 0; i < 3; i++) {
            System.out.println(V1.get(i) + " " + V2.get(i));
        }
 
    }
 
// Driver code
    public static void main(String[] args) {
        int xmid[] = {5, 4, 5};
        int ymid[] = {3, 4, 5};
        findVertex(xmid, ymid);
    }
}
// This code is contributed by
// PrinciRaj1992

Python3




# Python3 program to find coordinate of the
# triangle given midpoint of each side
 
N = 3
 
# Return after solving the equations and
# finding the vertices coordinate.
def solve(v):
 
    res = []
 
    # Finding sum of all three coordinate.
    all3 = v[0] + v[1] + v[2]
 
    # Solving the equation.
    res.append(all3 - v[1] * 2)
    res.append(all3 - v[2] * 2)
    res.append(all3 - v[0] * 2)
    return res
 
# Finds vertices of a triangles from given
# middle vertices.
def findVertex(xmid, ymid):
 
    # Find X coordinates of vertices.
    V1 = solve(xmid)
 
    # Find Y coordinates of vertices.
    V2 = solve(ymid)
 
    # Output the solution.
    for i in range(0, 3):
        print(V1[i], end=" ")
        print(V2[i])
 
# Driver code
if __name__=='__main__':
    xmid = [5, 4, 5]
    ymid = [3, 4, 5]
    findVertex(xmid, ymid)
 
# This code is contributed by
# Sanjit_Prasad

C#




// C# program to find coordinate of the
// triangle given midpoint of each side
using System;
using System.Collections;
 
class GFG
{
 
    //static final int N = 3;
    // Return after solving the equations and
    // finding the vertices coordinate.
    static ArrayList solve(int []v)
    {
        ArrayList res = new ArrayList();
 
        // Finding sum of all three coordinate.
        int all3 = v[0] + v[1] + v[2];
 
        // Solving the equation.
        res.Add(all3 - v[1] * 2);
        res.Add(all3 - v[2] * 2);
        res.Add(all3 - v[0] * 2);
 
        return res;
    }
 
    // Finds vertices of a triangles from given
    // middle vertices.
    static void findVertex(int []xmid, int []ymid)
    {
        // Find X coordinates of vertices.
        ArrayList V1 = solve(xmid);
 
        // Find Y coordinates of vertices.
        ArrayList V2 = solve(ymid);
 
        // Output the solution.
        for (int i = 0; i < 3; i++)
        {
            Console.WriteLine(V1[i] + " " + V2[i]);
        }
 
    }
 
    // Driver code
    public static void Main()
    {
        int []xmid = {5, 4, 5};
        int []ymid = {3, 4, 5};
        findVertex(xmid, ymid);
    }
}
 
// This code is contributed by mits

PHP




<?php
// PHP program to find coordinate of the
// triangle given midpoint of each side
 
$N = 3;
 
// Return after solving the equations and
// finding the vertices coordinate.
function solve($v)
{
    $res = array();
 
    // Finding sum of all three coordinate.
    $all3 = $v[0] + $v[1] + $v[2];
 
    // Solving the equation.
    array_push($res, $all3 - $v[1] * 2);
    array_push($res, $all3 - $v[2] * 2);
    array_push($res, $all3 - $v[0] * 2);
    return $res;
}
 
// Finds vertices of a triangles from
// given middle vertices.
function findVertex($xmid, $ymid)
{
    // Find X coordinates of vertices.
    $V1 = solve($xmid);
 
    // Find Y coordinates of vertices.
    $V2 = solve($ymid);
 
    // Output the solution.
    for ($i = 0; $i < 3; $i++)
        print($V1[$i] . " " .  
              $V2[$i] . "\n");
}
 
// Driver code
$xmid = array(5, 4, 5);
$ymid = array(3, 4, 5);
findVertex($xmid, $ymid)
 
// This code is contributed by mits
?>

Javascript




<script>
      // JavaScript program to find coordinate of the
      // triangle given midpoint of each side
      // Return after solving the equations and
      // finding the vertices coordinate.
      function solve(v) {
        var res = [];
 
        // Finding sum of all three coordinate.
        var all3 = v[0] + v[1] + v[2];
 
        // Solving the equation.
        res.push(all3 - v[1] * 2);
        res.push(all3 - v[2] * 2);
        res.push(all3 - v[0] * 2);
 
        return res;
      }
 
      // Finds vertices of a triangles from given
      // middle vertices.
      function findVertex(xmid, ymid) {
        // Find X coordinates of vertices.
        var V1 = solve(xmid);
 
        // Find Y coordinates of vertices.
        var V2 = solve(ymid);
 
        // Output the solution.
        for (var i = 0; i < 3; i++) {
          document.write(V1[i] + " " + V2[i] + "<br>");
        }
      }
 
      // Driver code
      var xmid = [5, 4, 5];
      var ymid = [3, 4, 5];
      findVertex(xmid, ymid);
    </script>

Output: 

6 4
4 2
4 6

Time Complexity: O(1)

This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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