Java Program to Check if Three Points are Collinear

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In the previous article, we have discussed Java Program to Find Slope of a Line

In this article we will see how to check if three points are collinear or not.

Java Program to Check if Three Points are Collinear

Before jumping into the program directly, let’s see first how we get the slope of a line.

Approach-1:

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

If formula for area of triangle is equal to zero then three points lie on a straight line.
Or, we can say 3 points are collinear.
Approach-2:

Slope of any pair of points :
(y3 - y2)/(x3 - x2) = (y2 - y1)/(x2 - x1)

When slope of any pair of points are same as other pair then three points lie on a straight line. 
Or, we can say 3 points are collinear.

Let’s see different ways to check three points are collinear or not.

Method-1: Java Program to Check if Three Points are Collinear By Finding Area of Triangle Formed

Approach:

  1. Take the value for three points.
  2. Find area of triangle formed by using formula 0.5 * [x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)]
  3. Check if the area of triangle formed is equal to zero then three points are collinear.

Program:

public class Main
{ 
    // Main method
    public static void main(String args[]) 
    { 
        double x1 = 1, x2 = 1, x3 = 1, 
            y1 = 1, y2 = 4, y3 = 5;
            
        //checkCollinear() method called to check 
        //if 3 points lie on a stright line or not.               
        checkCollinear(x1, y1, x2, y2, x3, y3);  
  
    } 
    
    // checkCollinear Method to check if point collinear or not 
    static void checkCollinear(double x1, double y1, double x2,  
                          double y2, double x3, double y3) 
    { 
          
        //calculating area
        double area = 0.5*(x1 * (y2 - y3) +  x2 * (y3 - y1) +  x3 * (y1 - y2)); 
        System.out.println("Area formed by triangle:"+area); 
      
        if (area == 0) 
            System.out.println("Area is equal to zero. So, 3 lines are collinear."); 
        else
            System.out.println("Area is not equal to zero. So, 3 lines are not collinear."); 
    }  
} 

Output:

Area formed by triangle: 0.0
Area is equal to zero. So, 3 lines are collinear.

Method-2: Java Program to Check if Three Points are Collinear By Finding Slope of Pairs

Approach:

  1. Take the value for three points.
  2. Check slope of any pair of point is equal to slope of other point i.e. ((y3 - y2) * (x2 - x1) == (y2 - y1) * (x3 - x2))
  3. If both slope are equal then three points are collinear.

Program:

import java.io.*; 
  
public class Main
{ 
  
    // Main Method
        public static void main (String[] args) 
        { 
            double x1 = 1, x2 = 1, x3 = 1,  
            y1 = 1, y2 = 4, y3 = 5;  
            //checkCollinear() method called to check 
            //if 3 points lie on a stright line or not.
           checkColliner(x1, y1, x2, y2, x3, y3);  
        } 
        
    // Methodn to check if 3 points collinear or not
    static void checkColliner(double x1, double y1, double x2, double y2, double x3, double y3)  
    {  
        if ((y3 - y2) * (x2 - x1) ==  (y2 - y1) * (x3 - x2))  
            System.out.println("Slope are equal. So, 3 lines are collinear.");
        else
           System.out.println("Slope are not equal. So, 3 lines are not collinear.");
    }  
      
}
Output:

Slope are equal. So, 3 lines are collinear.

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