一个点在另一点旋转 180 度时的反射

给定二维平面上的两点坐标(x ₁ , y ₁ )和(x ₂ , y ₂ ) 。任务是找到 (x ₁ , y ₁ ) 在 (x ₂ , y ₂ ) 旋转 180 度时的反射。
例子：

Input : x1 = 0, y1 = 0, x2 = 1, y2 = 1
Output : (2, 2)

Input : x1 = 1, y1 = 1, x2 = 2, y2 = 2
Output : (3, 3)

令(x ₁ , y ₁ )点关于(x ₂ , y ₂ )的反射点为(x’, y’)。
对于 (x’, y’) 是点 (x ₁ , y ₁ ) 围绕点 (x ₂ , y ₂ ) 的 180 度旋转，它们都必须共线，即所有三个点必须位于同一条直线上。此外，观察 (x ₂ , y ₂ ) 将成为 (x ₁ , y ₁ ) 和 (x’, y’) 之间的中点。

所以，
x’ – x ₂ = x ₂ – x ₁
y’ – y ₂ = y ₂ – y ₁
x’ = 2 * x ₂ – x ₁
y’ = 2 * y ₂ – y ₁
下面是这个方法的实现：

C++

// CPP Program tof find the 180 degree reflection
// of one point around another point.
#include 
using namespace std;
 
void findPoint(int x1, int y1, int x2, int y2)
{
    cout << "(" << 2 * x2 - x1 << ", "
         << 2 * y2 - y1 << ")";
}
 
 
int main()
{
    int x1 = 0, y1 = 0, x2 = 1, y2 = 1;
    findPoint(x1, y1, x2, y2);
    return 0;
}

Java

// Java Program to find the 180 degree
// reflection of one point around
// another point.
class GFG {
     
    static void findPoint(int x1, int y1,
                          int x2, int y2)
    {
        System.out.println("(" + (int)(2 * x2 - x1)
               + "," + (int)(2 * y2 - y1 ) + " )");
    }
     
    // Driver code
    public static void main(String args[])
    {
        int x1 = 0, y1 = 0, x2 = 1, y2 = 1;
         
        findPoint(x1, y1, x2, y2);
    }
}
 
// This code is contributed by Arnab Kundu.

Python3

# Python3 Program for find the 180
# degree reflection of one point
# around another point.
 
def findPoint(x1, y1, x2, y2):
    print("(" , 2 * x2 - x1 , ",",
                2 * y2 - y1 ,")");
 
# Driver Code
x1 = 0;
y1 = 0;
x2 = 1;
y2 = 1;
findPoint(x1, y1, x2, y2);
 
# This code is contributed by mits

C#

// C# Program to find the 180 degree reflection
// of one point around another point.
using System;
 
public class GFG {
     
    static void findPoint(int x1, int y1,
                          int x2, int y2)
    {
        Console.WriteLine("(" + (int)(2 * x2 - x1)
               + "," + (int)(2 * y2 - y1 ) + " )");
    }
     
    // Driver code
    static public void Main(String []args)
    {
        int x1 = 0, y1 = 0, x2 = 1, y2 = 1;
         
        findPoint(x1, y1, x2, y2);
    }
}
 
// This code is contributed by Arnab Kundu.

Javascript

 
// Javascript Program to find the 180 degree reflection
// of one point around another point.
 
function findPoint(x1, y1, x2, y2)
{
    document.write("(" + 2 * (x2 - x1) + ", "
        + 2 * (y2 - y1) + ")");
}
 
    let x1 = 0, y1 = 0, x2 = 1, y2 = 1;
    findPoint(x1, y1, x2, y2);
 
 
// This code is contributed by Mayank Tyagi
 

输出：

(2, 2)

时间复杂度： O(1)