# Program to check if three points are collinear

Given three points, check whether they lie on a straight (collinear) or not

Examples :

```Input : (1, 1), (1, 4), (1, 5)
Output : Yes
The points lie on a straight line

Input : (1, 5), (2, 5), (4, 6)
Output : No
The points do not lie on a straight line
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

First approach
Three points lie on the straight line if the area formed by the triangle of these three points is zero. So we will check if the area formed by the triangle is zero or not

```Formula for area of triangle is :
0.5 * [x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)]

The formula is basically half of determinant
value of following.
x1 x2 x3
y1 y2 y3
1   1  1

The above formula is derived from shoelace formula.
```

## C++

 `// C++ program to check if three ` `// points are collinear or not  ` `// using area of triangle. ` `#include ` `#include ` `#include ` ` `  `using` `namespace` `std; ` `// function to check if point  ` `// collinear or not ` `void` `collinear(``int` `x1, ``int` `y1, ``int` `x2,  ` `               ``int` `y2, ``int` `x3, ``int` `y3) ` `{ ` `    ``// Calculation the area of  ` `    ``// triangle. We have skipped  ` `    ``// multiplication with 0.5  ` `    ``// to avoid floating point  ` `    ``// computations  ` `    ``int` `a = x1 * (y2 - y3) +  ` `            ``x2 * (y3 - y1) +  ` `            ``x3 * (y1 - y2); ` ` `  `    ``if` `(a == 0) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `x1 = 1, x2 = 1, x3 = 1,  ` `        ``y1 = 1, y2 = 4, y3 = 5; ` `    ``collinear(x1, y1, x2, y2, x3, y3); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed ` `// by Akanksha Rai(Abby_akku) `

## C

 `// C program to check if three ` `// points are collinear or not  ` `// using area of triangle. ` `#include ` `#include ` `#include ` ` `  `// function to check if point  ` `// collinear or not ` `void` `collinear(``int` `x1, ``int` `y1, ``int` `x2,  ` `               ``int` `y2, ``int` `x3, ``int` `y3) ` `{ ` `    ``// Calculation the area of  ` `    ``// triangle. We have skipped  ` `    ``// multiplication with 0.5  ` `    ``// to avoid floating point  ` `    ``// computations  ` `    ``int` `a = x1 * (y2 - y3) +  ` `            ``x2 * (y3 - y1) +  ` `            ``x3 * (y1 - y2); ` ` `  `    ``if` `(a == 0) ` `        ``printf``(``"Yes"``); ` `    ``else` `        ``printf``(``"No"``); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `x1 = 1, x2 = 1, x3 = 1,  ` `        ``y1 = 1, y2 = 4, y3 = 5; ` `    ``collinear(x1, y1, x2, y2, x3, y3); ` `    ``return` `0; ` `} `

## Java

 `// Java program to check if  ` `// three points are collinear ` `// or not using area of triangle. ` `class` `GFG  ` `{ ` `     `  `    ``// function to check if  ` `    ``// point collinear or not ` `    ``static` `void` `collinear(``int` `x1, ``int` `y1, ``int` `x2,  ` `                          ``int` `y2, ``int` `x3, ``int` `y3) ` `    ``{ ` `         `  `        ``/* Calculation the area of  ` `        ``triangle. We have skipped  ` `        ``multiplication with 0.5  ` `        ``to avoid floating point  ` `        ``computations */` `        ``int` `a = x1 * (y2 - y3) +  ` `                ``x2 * (y3 - y1) +  ` `                ``x3 * (y1 - y2); ` `     `  `        ``if` `(a == ``0``) ` `            ``System.out.println(``"Yes"``); ` `        ``else` `            ``System.out.println(``"No"``); ` `    ``}  ` `         `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `x1 = ``1``, x2 = ``1``, x3 = ``1``, ` `            ``y1 = ``1``, y2 = ``4``, y3 = ``5``; ` `                             `  `        ``collinear(x1, y1, x2, y2, x3, y3);  ` ` `  `    ``} ` `} ` ` `  `// This code is contributed by Sam007. `

/div>

## Python

 `# Python program to check ` `# if three points are collinear ` `# or not using area of triangle. ` ` `  `# function to check if  ` `# point collinear or not ` `def` `collinear(x1, y1, x2, y2, x3, y3): ` `     `  `    ``""" Calculation the area of   ` `        ``triangle. We have skipped  ` `        ``multiplication with 0.5 to ` `        ``avoid floating point computations """` `    ``a ``=` `x1 ``*` `(y2 ``-` `y3) ``+` `x2 ``*` `(y3 ``-` `y1) ``+` `x3 ``*` `(y1 ``-` `y2) ` ` `  `    ``if` `(a ``=``=` `0``): ` `        ``print` `"Yes"` `    ``else``: ` `        ``print` `"No"` ` `  `# Driver Code ` `x1, x2, x3, y1, y2, y3 ``=` `1``, ``1``, ``1``, ``1``, ``4``, ``5` `collinear(x1, y1, x2, y2, x3, y3) ` ` `  `# This code is contributed ` `# by Sachin Bisht `

## C#

 `// C# program to check if  ` `// three points are collinear ` `// or not using area of triangle. ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``/* function to check if  ` `    ``point collinear or not */` `    ``static` `void` `collinear(``int` `x1, ``int` `y1, ``int` `x2,  ` `                          ``int` `y2, ``int` `x3, ``int` `y3) ` `    ``{ ` `         `  `        ``/* Calculation the area of   ` `        ``triangle. We have skipped  ` `        ``multiplication with 0.5 to  ` `        ``avoid floating point computations */` `        ``int` `a = x1 * (y2 - y3) +  ` `                ``x2 * (y3 - y1) +  ` `                ``x3 * (y1 - y2); ` `     `  `        ``if` `(a == 0) ` `            ``Console.Write(``"Yes"``); ` `        ``else` `            ``Console.Write(``"No"``); ` `    ``}  ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main () ` `    ``{ ` `        ``int` `x1 = 1, x2 = 1, x3 = 1,  ` `            ``y1 = 1, y2 = 4, y3 = 5; ` `                             `  `        ``collinear(x1, y1, x2, y2, x3, y3); ` `    ``} ` `} ` ` `  `// This code is contributed by Sam007. `

## PHP

 ` `

Output :

```Yes
```

Second approach

```For three points, slope of any pair of points
must be same as other pair.

For example, slope of line joining (x2, y2)
and (x3, y3), and line joining (x1, y1) and
(x2, y2) must be same.

(y3 - y2)/(x3 - x2) = (y2 - y1)/(x2 - x1)

In other words,
(y3 - y2)(x2 - x1) = (y2 - y1)(x3 - x2) ```

If this equals zero then points lie on a straight line

## C

 `// Slope based solution to check  ` `// if three points are collinear.  ` `#include ` `#include ` ` `  `/* function to check if  ` `point collinear or not*/` `void` `collinear(``int` `x1, ``int` `y1, ``int` `x2,  ` `               ``int` `y2, ``int` `x3, ``int` `y3) ` `{ ` `    ``if` `((y3 - y2) * (x2 - x1) ==  ` `        ``(y2 - y1) * (x3 - x2)) ` `        ``printf``(``"Yes"``); ` `    ``else` `        ``printf``(``"No"``); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `x1 = 1, x2 = 1, x3 = 0,  ` `        ``y1 = 1, y2 = 6, y3 = 9; ` `    ``collinear(x1, y1, x2, y2, x3, y3); ` `    ``return` `0; ` `} `

## Java

 `// Slope based solution to check  ` `// if three points are collinear.  ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  `/* function to check if  ` `point collinear or not*/` `static` `void` `cool_line(``int` `x1, ``int` `y1, ``int` `x2,  ` `            ``int` `y2, ``int` `x3, ``int` `y3)  ` `{  ` `    ``if` `((y3 - y2) * (x2 - x1) ==  ` `        ``(y2 - y1) * (x3 - x2))  ` `        ``System.out.println(``"Yes"``);  ` `    ``else` `        ``System.out.println(``"No"``);  ` `}  ` ` `  `// Driver Code  ` `     `  `    ``public` `static` `void` `main (String[] args) { ` `        ``int` `a1 = ``1``, a2 = ``1``, a3 = ``0``,  ` `        ``b1 = ``1``, b2 = ``6``, b3 = ``9``;  ` `       ``cool_line(a1, b1, a2, b2, a3, b3);  ` `         `  `         `  `    ``} ` `} ` `//This Code is Contributed by ajit `

## Python

 `# Slope based solution to check if three ` `# points are collinear.  ` `  `  `# function to check if ` `# point collinear or not ` `def` `collinear(x1, y1, x2, y2, x3, y3): ` `    `  `    ``if` `((y3 ``-` `y2)``*``(x2 ``-` `x1) ``=``=` `(y2 ``-` `y1)``*``(x3 ``-` `x2)): ` `        ``print` `(``"Yes"``) ` `    ``else``: ` `        ``print` `(``"No"``) ` `  `  `# Driver Code  ` `x1, x2, x3, y1, y2, y3 ``=` `1``, ``1``, ``0``, ``1``, ``6``, ``9` `collinear(x1, y1, x2, y2, x3, y3); ` ` `  `# This code is contributed  ` `# by Sachin Bisht `

## C#

 `// Slope based solution to check  ` `// if three points are collinear.  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `/* function to check if  ` `point collinear or not*/` `static` `void` `cool_line(``int` `x1, ``int` `y1, ``int` `x2,  ` `                      ``int` `y2, ``int` `x3, ``int` `y3)  ` `{  ` `    ``if` `((y3 - y2) * (x2 - x1) ==  ` `        ``(y2 - y1) * (x3 - x2))  ` `        ``Console.WriteLine(``"Yes"``);  ` `    ``else` `        ``Console.WriteLine(``"No"``);  ` `}  ` ` `  `// Driver Code  ` `static` `public` `void` `Main () ` `{ ` `    ``int` `a1 = 1, a2 = 1, a3 = 0,  ` `    ``b1 = 1, b2 = 6, b3 = 9;  ` `    ``cool_line(a1, b1, a2, b2, a3, b3);  ` `}  ` `}  ` ` `  `// This code is contributed by ajit  `

## PHP

 ` `

Output :

```No
```

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## tags:

Geometric Geometric