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Check whether a straight line can be formed using N co-ordinate points
• Difficulty Level : Medium
• Last Updated : 21 May, 2021

Given an array arr[] of N co-ordinate points, the task is to check whether a straight line can be formed using these co-ordinate points.

Input: arr[] = {{0, 0}, {1, 1}, {2, 2}}
Output: Yes
Explanation:
Slope of every two points is same. That is 1.
Therefore, a straight line can be formed using these points.

Input: arr[] = {{0, 1}, {2, 0}}
Output: Yes
Explanation:
Two points in co-ordinate system always forms a straight line.

Approach: The idea is to find the slope of line between every pair of points in the array and if the slope of every pair of point is same, then these points together forms a straight line.

```// Slope of line formed by
// two points (y2, y1), (x2, x1)

Slope of Line = y2 - y1
---------
x2 - x1```

Below is the implementation of the above approach:

## C++

 `// C++ implementation to check``// if a straight line``// can be formed using N points` `#include ` `using` `namespace` `std;` `// Function to check if a straight line``// can be formed using N points``bool` `isStraightLinePossible(``    ``vector > arr, ``int` `n)``{``    ``// First pair of point (x0, y0)``    ``int` `x0 = arr.first;``    ``int` `y0 = arr.second;` `    ``// Second pair of point (x1, y1)``    ``int` `x1 = arr.first;``    ``int` `y1 = arr.second;` `    ``int` `dx = x1 - x0, dy = y1 - y0;``    ` `    ``// Loop to iterate over the points``    ``for` `(``int` `i = 0; i < n; i++) {``        ``int` `x = arr[i].first, y = arr[i].second;``        ``if` `(dx * (y - y1) != dy * (x - x1)){``            ``cout << ``"NO"``;``            ``return` `false``;``        ``}``    ``}``    ``cout << ``"YES"``;``    ``return` `true``;``}` `// Driver Code``int` `main()``{``    ``// Array of points``    ``vector > arr =``    ``{ { 0, 0 }, { 1, 1 }, { 3, 3 }, { 2, 2 } };``    ``int` `n = 4;``    ` `    ``// Function Call``    ``isStraightLinePossible(arr, n);``    ``return` `0;``}`

## Java

 `// Java implementation to check``// if a straight line can be``// formed using N points``import` `java.util.*;` `class` `GFG{` `static` `class` `pair``{``    ``int` `first, second;``    ``pair(``int` `first, ``int` `second)``    ``{``        ``this``.first = first;``        ``this``.second = second;``    ``}``}` `// Function to check if a straight line``// can be formed using N points``static` `void` `isStraightLinePossible(``       ``ArrayList arr, ``int` `n)``{``    ` `    ``// First pair of point (x0, y0)``    ``int` `x0 = arr.get(``0``).first;``    ``int` `y0 = arr.get(``0``).second;` `    ``// Second pair of point (x1, y1)``    ``int` `x1 = arr.get(``1``).first;``    ``int` `y1 = arr.get(``1``).second;` `    ``int` `dx = x1 - x0, dy = y1 - y0;` `    ``// Loop to iterate over the points``    ``for``(``int` `i = ``0``; i < n; i++)``    ``{``        ``int` `x = arr.get(i).first;``        ``int` `y = arr.get(i).second;``        ``if` `(dx * (y - y1) != dy * (x - x1))``        ``{``            ``System.out.println(``"NO"``);``        ``}``    ``}``    ``System.out.println(``"YES"``);``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Array of points``    ``ArrayList arr = ``new` `ArrayList<>();``    ``arr.add(``new` `pair(``0``, ``0``));``    ``arr.add(``new` `pair(``1``, ``1``));``    ``arr.add(``new` `pair(``3``, ``3``));``    ``arr.add(``new` `pair(``2``, ``2``));` `    ``int` `n = ``4``;` `    ``// Function Call``    ``isStraightLinePossible(arr, n);``}``}` `// This code is contributed by offbeat`

## Python3

 `# Python3 implementation to check``# if a straight line can be formed``# using N points` `# Function to check if a straight line``# can be formed using N points``def` `isStraightLinePossible(arr, n):``    ` `    ``# First pair of point (x0, y0)``    ``x0 ``=` `arr[``0``][``0``]``    ``y0 ``=` `arr[``0``][``1``]` `    ``# Second pair of point (x1, y1)``    ``x1 ``=` `arr[``1``][``0``]``    ``y1 ``=` `arr[``1``][``1``]` `    ``dx ``=` `x1 ``-` `x0``    ``dy ``=` `y1 ``-` `y0``    ` `    ``# Loop to iterate over the points``    ``for` `i ``in` `range``(n):``        ``x ``=` `arr[i][``0``]``        ``y ``=` `arr[i][``1``]``        ` `        ``if` `(dx ``*` `(y ``-` `y1) !``=` `dy ``*` `(x ``-` `x1)):``            ``print``(``"NO"``, end ``=` `"")``            ``return` `False` `    ``print``(``"YES"``, end ``=` `"")``    ``return` `True` `# Driver code` `# Array of points``arr ``=` `[ [ ``0``, ``0` `], [ ``1``, ``1` `],``        ``[ ``3``, ``3` `], [ ``2``, ``2` `] ]``n ``=` `4` `# Function Call``isStraightLinePossible(arr, n)` `# This code is contributed by divyeshrabadiya07`

## C#

 `// C# implementation to check``// if a straight line can be``// formed using N points``using` `System;``using` `System.Collections.Generic;` `class` `GFG{` `public` `class` `pair``{``    ``public` `int` `first, second;``    ``public` `pair(``int` `first, ``int` `second)``    ``{``        ``this``.first = first;``        ``this``.second = second;``    ``}``}` `// Function to check if a straight line``// can be formed using N points``static` `void` `isStraightLinePossible(``    ``List arr, ``int` `n)``{``    ` `    ``// First pair of point (x0, y0)``    ``int` `x0 = arr.first;``    ``int` `y0 = arr.second;` `    ``// Second pair of point (x1, y1)``    ``int` `x1 = arr.first;``    ``int` `y1 = arr.second;` `    ``int` `dx = x1 - x0, dy = y1 - y0;` `    ``// Loop to iterate over the points``    ``for``(``int` `i = 0; i < n; i++)``    ``{``        ``int` `x = arr[i].first;``        ``int` `y = arr[i].second;``        ` `        ``if` `(dx * (y - y1) != dy * (x - x1))``        ``{``            ``Console.WriteLine(``"NO"``);``        ``}``    ``}``    ``Console.WriteLine(``"YES"``);``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ` `    ``// Array of points``    ``List arr = ``new` `List();``    ` `    ``arr.Add(``new` `pair(0, 0));``    ``arr.Add(``new` `pair(1, 1));``    ``arr.Add(``new` `pair(3, 3));``    ``arr.Add(``new` `pair(2, 2));` `    ``int` `n = 4;` `    ``// Function call``    ``isStraightLinePossible(arr, n);``}``}` `// This code is contributed by Princi Singh`

## Javascript

 ``
Output:
`YES`

Time Complexity: O(N)

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