Skip to content
Related Articles

Related Articles

Check whether triangle is valid or not if three points are given
  • Difficulty Level : Basic
  • Last Updated : 25 Mar, 2021

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. 
\text{Area of Triangle }= \frac{1}{2}*(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
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 <bits/stdc++.h>
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




<script>
// Javascript implementation to check
// if three points form a triangle
 
// Function to check if three
// points make a triangle
function checkTriangle(x1, y1, x2,
                y2, x3, y3)
{
 
    // Calculation the area of
    // triangle. We have skipped
    // multiplication with 0.5
    // to avoid floating point
    // computations
    let a = x1 * (y2 - y3)
            + x2 * (y3 - y1)
            + x3 * (y1 - y2);
 
    // Condition to check if
    // area is not equal to 0
    if (a == 0)
        document.write("No");
    else
        document.write("Yes");
}
 
// Driver Code
    let x1 = 1, x2 = 2, x3 = 3,
        y1 = 1, y2 = 2, y3 = 3;
    checkTriangle(x1, y1, x2,
                y2, x3, y3);
     
// This code is contributed by Mayank Tyagi
 
</script>
Output: 
No

 

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.




My Personal Notes arrow_drop_up
Recommended Articles
Page :