# Find coordinates of the triangle given midpoint of each side

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:

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#define N 3using namespace std; // Return after solving the equations and// finding the vertices coordinate.vector solve(int v[]){    vector 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 V1 = solve(xmid);     // Find Y coordinates of vertices.    vector V2 = solve(ymid);     // Output the solution.    for (int i = 0; i < 3; i++)        cout << V1[i] << " "             << V2[i] <

## 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 solve(int v[]) {        Vector res = new Vector();         // 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 V1 = solve(xmid);         // Find Y coordinates of vertices.         Vector 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 codeif __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



## Javascript



Output:

6 4
4 2
4 6

Time Complexity: O(1)

Auxiliary Space: O(1) because it is using constant space

Previous
Next