# Section formula for 3 D

Given two coordinates (x1, y1, z1) and (x2, y2, z2) in 3D, and m and n, find the co-ordinates that divides the line joining (x1, y1, Z1) and (x2, y2, Z2) in the ratio m : n.

Examples:

Input : x1 = 2, y1 = -1, Z1 = 4, x2 = 4, y2 = 3, Z2 = 2,
m = 2, n = 3
Output : (2.8, .6, 3.2)

Explanation: co-ordinates (2.8, .6, 3.2)
divides the line in ratio 2 : 3

## Recommended: Please try your approach on {IDE} first, before moving on to the solution. Approach:
Given two coordinates A(x1, y1, Z1) and B(x2, y2, Z2) in 3D, and m and n, we have to find the co-ordinates that divides the line joining (x1, y1, Z1) and (x2, y2, Z2) in the ratio m : n.
Let the co-ordinates will be P(x, y, z)
then according to section fORmula in 3 D
x = (m * x2 + n * x1) / (m + n)
y = (m * y2 + n * y1) / (m + n)
z = (m * z2 + n * z1) / (m + n)

Below is the implementation of above approach:

## C++

 `// CPP program to find point that divides ` `// given line in given ratio in 3D. ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the section of the line ` `void` `section(``double` `x1, ``double` `x2, ``double` `y1, ` `             ``double` `y2, ``double` `z1, ``double` `z2, ` `             ``double` `m, ``double` `n) ` `{ ` `    ``// Applying section formula ` `    ``double` `x = ((m * x2) + (n * x1)) / (m + n); ` ` `  `    ``double` `y = ((m * y2) + (n * y1)) / (m + n); ` ` `  `    ``double` `z = ((m * z2) + (n * z1)) / (m + n); ` ` `  `    ``// Printing result ` `    ``cout << ``"("` `<< x << ``", "``; ` `    ``cout << y << ``", "``; ` `    ``cout << z << ``")"` `<< endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``double` `x1 = 2, x2 = 4, y1 = -1, ` `           ``y2 = 3, z1 = 4, z2 = 2, ` `           ``m = 2, n = 3; ` `    ``section(x1, x2, y1, y2, z1, z2, m, n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find point that divides ` `// given line in given ratio in 3D. ` `import` `java.util.*; ` ` `  `class` `solution ` `{ ` ` `  `// Function to find the section of the line ` `static` `void` `section(``double` `x1, ``double` `x2, ``double` `y1, ` `            ``double` `y2, ``double` `z1, ``double` `z2, ` `            ``double` `m, ``double` `n) ` `{ ` `    ``// Applying section formula ` `    ``double` `x = ((m * x2) + (n * x1)) / (m + n); ` ` `  `    ``double` `y = ((m * y2) + (n * y1)) / (m + n); ` ` `  `    ``double` `z = ((m * z2) + (n * z1)) / (m + n); ` ` `  `    ``System.out.print( ``"("` `+x +``", "``); ` `    ``System.out.print( y+ ``", "``); ` `    ``System.out.println(z + ``")"` `); ` ` `  `} ` ` `  `// Driver code ` `public` `static` `void` `main(String arr[]) ` `{ ` `    ``double` `x1 = ``2``, x2 = ``4``, y1 = -``1``, ` `        ``y2 = ``3``, z1 = ``4``, z2 = ``2``, ` `        ``m = ``2``, n = ``3``; ` `    ``section(x1, x2, y1, y2, z1, z2, m, n); ` ` `  `} ` ` `  `} ` `//This code is contributed by Surendra_Gangwar `

## Python3

 `# Python 3 program to find point that divides ` `# given line in given ratio in 3D. ` ` `  `# Function to find the section of the line ` `def` `section(x1, x2, y1, y2, z1, z2, m, n): ` `    ``# Applying section formula ` `    ``x ``=` `((m ``*` `x2) ``+` `(n ``*` `x1)) ``/` `(m ``+` `n) ` ` `  `    ``y ``=` `((m ``*` `y2) ``+` `(n ``*` `y1)) ``/` `(m ``+` `n) ` ` `  `    ``z ``=` `((m ``*` `z2) ``+` `(n ``*` `z1)) ``/` `(m ``+` `n) ` ` `  `    ``# Printing result ` `    ``print``(``"("``,x,``","``,y,``","``,z,``")"``) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``x1 ``=` `2` `    ``x2 ``=` `4` `    ``y1 ``=` `-``1` `    ``y2 ``=` `3` `    ``z1 ``=` `4` `    ``z2 ``=` `2` `    ``m ``=` `2` `    ``n ``=` `3` `    ``section(x1, x2, y1, y2, z1, z2, m, n) ` ` `  `#This code is contributed by  ` `# Surendra_Gangwar `

## C#

 `// C# program to find point that divides  ` `// given line in given ratio in 3D.  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to find the section ` `// of the line  ` `static` `void` `section(``double` `x1, ``double` `x2, ``double` `y1,  ` `                    ``double` `y2, ``double` `z1, ``double` `z2,  ` `                    ``double` `m, ``double` `n)  ` `{  ` `    ``// Applying section formula  ` `    ``double` `x = ((m * x2) + (n * x1)) / (m + n);  ` ` `  `    ``double` `y = ((m * y2) + (n * y1)) / (m + n);  ` ` `  `    ``double` `z = ((m * z2) + (n * z1)) / (m + n);  ` ` `  `    ``Console.Write(``"("` `+ x +``", "``);  ` `    ``Console.Write(y + ``", "``);  ` `    ``Console.WriteLine(z + ``")"` `);  ` `}  ` ` `  `// Driver code  ` `static` `public` `void` `Main () ` `{ ` `    ``double` `x1 = 2, x2 = 4, y1 = -1,  ` `    ``y2 = 3, z1 = 4, z2 = 2,  ` `    ``m = 2, n = 3;  ` `    ``section(x1, x2, y1, y2, z1, z2, m, n);  ` `}  ` `}  ` ` `  `// This code is contributed by ajit.  `

## PHP

 `

Output:

```(2.8, 0.6, 3.2)
```

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