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# Check whether triangle is valid or not if three points are given

• Difficulty Level : Basic
• Last Updated : 14 Jun, 2022

Given coordinates of three points in a plane P1, P2 and P3, the task is to check if the three points form a triangle or not
Examples:

Input: P1 = (1, 5), P2 = (2, 5), P3 = (4, 6)
Output: Yes
Input: P1 = (1, 1), P2 = (1, 4), P3 = (1, 5)
Output: No

Approach: The key observation in the problem is three points form a triangle only when they don’t lie on the straight line, that is an area formed by the triangle of these three points is not equal to zero.

The above formula is derived from shoelace formula.
So we will check if the area formed by the triangle is zero or not.
Below is the implementation of the above approach:

## C++

 // C++ implementation to check // if three points form a triangle   #include  using namespace std;   // Function to check if three // points make a triangle void checkTriangle(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);       // Condition to check if     // area is not equal to 0     if (a == 0)         cout << "No";     else         cout << "Yes"; }   // Driver Code int main() {     int x1 = 1, x2 = 2, x3 = 3,         y1 = 1, y2 = 2, y3 = 3;     checkTriangle(x1, y1, x2,                   y2, x3, y3);     return 0; }

## Java

 // Java implementation to check // if three points form a triangle import java.io.*;  import java.util.*;    class GFG {        // Function to check if three // points make a triangle static void checkTriangle(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);       // Condition to check if     // area is not equal to 0     if (a == 0)         System.out.println("No");     else         System.out.println("Yes"); }   // Driver code  public static void main(String[] args)  {      int x1 = 1, y1 = 1,         x2 = 2, y2 = 2,         x3 = 3, y3 = 3;     checkTriangle(x1, y1, x2, y2, x3, y3); }  }    // This code is contributed by coder001

## Python3

 # Python3 implementation to check  # if three points form a triangle    # Function to check if three  # points make a triangle  def checkTriangle(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))               # Condition to check if      # area is not equal to 0      if a == 0:         print('No')     else:         print('Yes')           # Driver code  if __name__=='__main__':           (x1, x2, x3) = (1, 2, 3)     (y1, y2, y3) = (1, 2, 3)           checkTriangle(x1, y1, x2, y2, x3, y3)       # This code is contributed by rutvik_56

## C#

 // C# implementation to check // if three points form a triangle using System;   class GFG {        // Function to check if three // points make a triangle static void checkTriangle(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);       // Condition to check if     // area is not equal to 0     if (a == 0)         Console.WriteLine("No");     else         Console.WriteLine("Yes"); }   // Driver code  public static void Main()  {      int x1 = 1, y1 = 1,         x2 = 2, y2 = 2,         x3 = 3, y3 = 3;               checkTriangle(x1, y1, x2, y2, x3, y3); }  }   //This code is contributed by AbhiThakur

## Javascript

 

Output:

No

Time Complexity: O(1)

Auxiliary Space : O(1)

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