求圆中直径的另一端坐标-yiteyi-C++库

给定圆直径的中心坐标（c1，c2）和一个坐标（x1，y1），找到直径的另一端坐标点（x2，y2）。

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图片[1]-求圆中直径的另一端坐标-yiteyi-C++库

例如：

Input  : x1 = –1, y1 = 2, and c1 = 3, c2 = –6Output : x2 = 7, y2 = -14Input  : x1 = 6.4, y1 = 3 and c1 = –10.7, c2 = 4Output : x2 = -27.8, y2 = 5

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

中点公式： 两端坐标点（x1，y2）和（x2，y2）的中点是点M，可通过以下方法找到： $M = frac{x_{1} + x_{2}}{2}, frac{y_{1} + y_{2}}{2}$

我们需要a（x2，y2）坐标，所以我们将中点应用到公式中

          c₁ = ((x₁+x₂)/2),  c2 = ((y₁+y₂)/2)          2*c₁ = (x₁+x₂),  2*c2 = (y₁+y₂)          x_{2 = (2*c1 - x1),  y2 = (2*c2 - y1)}

C++

                         // CPP program to find the                       
                         // other-end point of diameter                       
                         #include <iostream>                       
                         using                                     namespace                                     std;                       
           
                         // function to find the                       
                         // other-end point of diameter                       
                         void                                     endPointOfDiameterofCircle(                                     int                                     x1,                       
                                                 int                                     y1,                                     int                                     c1,                                     int                                     c2)                       
                         {                       
                                                 // find end point for x coordinates                       
                                                 cout <<                                     "x2 = "                       
                                                 << (                                     float                                     )(2 * c1 - x1)<<                                     "  "                                     ;                       
                                   
                                                 // find end point for y coordinates                       
                                                 cout <<                                     "y2 = "                                     << (                                     float                                     )(2 * c2 - y1);                       
                                   
                         }                       
                         // Driven Program                       
                         int                                     main()                       
                         {                       
                                                 int                                     x1 = -4, y1 = -1;                       
                                                 int                                     c1 = 3, c2 = 5;                       
                                   
                                                 endPointOfDiameterofCircle(x1, y1, c1, c2);                       
                                   
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find the other-end point of                       
                         // diameter                       
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
                                   
                                                 // function to find the other-end point of                       
                                                 // diameter                       
                                                 static                                     void                                     endPointOfDiameterofCircle(                                     int                                     x1,                       
                                                 int                                     y1,                                     int                                     c1,                                     int                                     c2)                       
                                                 {                       
                                   
                                                 // find end point for x coordinates                       
                                                 System.out.print(                                     "x2 = "                       
                                                 + (                                     2                                     * c1 - x1) +                                     " "                                     );                       
                                   
                                                 // find end point for y coordinates                       
                                                 System.out.print(                                     "y2 = "                                     + (                                     2                                     * c2 - y1));                       
                                                 }                       
                                   
                                                 // Driven Program                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     x1 = -                                     4                                     , y1 = -                                     1                                     ;                       
                                                 int                                     c1 =                                     3                                     , c2 =                                     5                                     ;                       
                                   
                                                 endPointOfDiameterofCircle(x1, y1, c1, c2);                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

Python3

                         # Python3 program to find the                       
                         # other-end point of diameter                       
           
                         # function to find the                       
                         # other-end point of diameter                       
                         def                                     endPointOfDiameterofCircle(x1, y1, c1, c2):                       
           
                                                 # find end point for x coordinates                       
                                                 print                                     (                                     "x2 ="                                     , (                                     2                                     *                                     c1                                     -                                     x1), end                                     =                                     " "                                     )                       
                                   
                                                 # find end point for y coordinates                       
                                                 print                                     (                                     "y2 ="                                     , (                                     2                                     *                                     c2                                     -                                     y1))                       
                                   
                         # Driven Program                       
                         x1                                     =                                     -                                     4                       
                         y1                                     =                                     -                                     1                       
                         c1                                     =                                     3                       
                         c2                                     =                                     5                       
                                   
                         endPointOfDiameterofCircle(x1, y1, c1, c2)                       
                                   
                         # This code is contributed by Smitha.                       

C#

                         // C# program to find the other -                       
                         // end point of diameter                       
                         using                                     System;                       
                         class                                     GFG {                       
                                   
                                                 // function to find the other - end                       
                                                 // point of  diameter                       
                                                 static                                     void                                     endPointOfDiameterofCircle(                                     int                                     x1,                       
                                                 int                                     y1,                       
                                                 int                                     c1,                       
                                                 int                                     c2)                       
                                                 {                       
                                                 // find end point for x coordinates                       
                                                 Console.Write(                                     "x2 = "                                     + (2 * c1 - x1) +                                     " "                                     );                       
                                   
                                                 // find end point for y coordinates                       
                                                 Console.Write(                                     "y2 = "                                     + (2 * c2 - y1));                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main ()                       
                                                 {                       
                                                 int                                     x1 = -4, y1 = -1;                       
                                                 int                                     c1 = 3, c2 = 5;                       
                                   
                                                 endPointOfDiameterofCircle(x1, y1, c1, c2);                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

PHP

                         <?php                       
                         // PHP program to find the                       
                         // other-end point of diameter                       
           
                         // function to find the                       
                         // other-end point of diameter                       
                         function                                     endPointOfDiameterofCircle(                                     $x1                                     ,                       
                                                 $y1                                     ,                                     $c1                                     ,                                     $c2                                     )                       
                         {                       
                                                 // find end point for x coordinates                       
                                                 echo                                     "x2 = "                                     ,(2 *                                     $c1                                     -                                     $x1                                     ),                                     " "                                     ;                       
                                   
                                                 // find end point for y coordinates                       
                                                 echo                                     "y2 = "                                     , (2 *                                     $c2                                     -                                     $y1                                     );                       
                         }                       
           
                         // Driven Program                       
                         $x1                                     = -4;                       
                         $y1                                     = -1;                       
                         $c1                                     = 3;                       
                         $c2                                     = 5;                       
                                   
                         endPointOfDiameterofCircle(                                     $x1                                     ,                                     $y1                                     ,                       
                                                 $c1                                     ,                                     $c2                                     );                       
           
                         // This code is contributed by Smitha                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find the                       
                         // other-end point of diameter                       
           
                         // Function to find the                       
                         // other-end point of diameter                       
                         function                                     endPointOfDiameterofCircle(x1, y1, c1, c2)                       
                         {                       
                                   
                                                 // Find end point for x coordinates                       
                                                 document.write(                                     "x2 = "                                     + (2 * c1 - x1) +                                     "  "                                     );                       
                                   
                                                 // Find end point for y coordinates                       
                                                 document.write(                                     "y2 = "                                     + (2 * c2 - y1));                       
                                   
                         }                       
           
                         // Driver code                       
                         let x1 = -4, y1 = -1;                       
                         let c1 = 3, c2 = 5;                       
           
                         endPointOfDiameterofCircle(x1, y1, c1, c2);                       
           
                         // This code is contributed by jana_sayantan                       
                                   
                         </script>                       

输出

x2 = 10 y2 = 11

类似地，如果我们给出一个直径的中心（c1，c2）和另一端坐标（x2，y2），我们找到一个（x1，y1）坐标

 Proof for (x1, y1) :          c1 = ((x1+x2)/2),  c2 = ((y1+y2)/2)          2*c1 = (x1+x2),  2*c2 = (y1+y2)          x1 = (2*c1 - x2),  y1 = (2*c2 - y2)

所以直径的另一端坐标（x1，y1）是

         x1 = (2*c1 - x2),  y1 = (2*c2 - y2)

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