检查三角形是否有效(如果给出了三个点)

给定平面P1 ， P2和P3中三个点的坐标，任务是检查三个点是否形成三角形
例子：

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

方法：问题中的关键观察结果是只有当三个点不位于直线上时它们才形成三角形，也就是说，这三个点的三角形所形成的面积不等于零。
$\text{Area of Triangle }= \frac{1}{2}*(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))$
上述公式是从鞋带公式中得出的。
因此，我们将检查三角形形成的面积是否为零。
下面是上述方法的实现：

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

// 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
 

输出：

No