在给定每一边的中点的情况下找到三角形的坐标

给定三个坐标(x，y)，它们是三角形边的中点。任务是找到三角形的坐标。
例子：

输入：midx ₁ = 5，midy ₁ = 3 midx ₂ = 4，midy ₂ = 4 midx ₃ = 5，midy ₃ = 5输出：x ₁ = 4 y ₁ = 2 x ₂ = 4 y ₂ = 6 x ₃ = 6年₃ = 4 解决方案可以通过图中验证。

让我们分别求解X坐标和Y坐标。对于顶点的X坐标，将其设为x ₁ ，x ₂ ，x ₃ 。然后，中点的X坐标将为(x ₁ + x ₂ )/ 2，(x ₂ + x ₃ )/ 2，(x ₃ + x ₁ )/ 2。观察到，这三个表达式的总和等于X坐标的总和。现在，我们有3个变量的总和以及每对变量的总和的3个表达式，通过求解方程来找出坐标值。
同样，我们求解Y坐标。

以下是此方法的实现：

C++

// C++ program to find coordinate of the
// triangle given midpoint of each side
#include
#define N 3
using 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 verices.
    vector V1 = solve(xmid);
  
    // Find Y coordinates of verices.
    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 verices. 
        Vector V1 = solve(xmid);
  
        // Find Y coordinates of verices. 
        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 verices.
    V1 = solve(xmid)
  
    # Find Y coordinates of verices.
    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 verices. 
        ArrayList V1 = solve(xmid); 
  
        // Find Y coordinates of verices. 
        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

输出：

6 4
4 2
4 6

时间复杂度： O(1)