/*  Name:  Richard Fox
    Class:  CSC 260.002
    Date:  8/17/16
*/

/*  Description: This program determines if 3 input points form a right triangle or      not.  After inputting the 3 points as x,y cartesian coordinates (6 variables),
    the program computes the length of each side using the Euclidean distance
    formula and then uses the Pythagorean theorem on the 3 sides to determine
    if the triangle is a right triangle or not.  The Euclidean distance formula
    is:  length = square root((point1 x - point2 x)^2 + (point1 y - point2 y)^2).
 	
    The Pythagoream theorem says if the three sides are a, b and c with a being the
    longest (hypotenuse) then if a^2 = b^2 + c^2 then the triangle is a right
    triangle.  Given 3 sides, s1, s2, s3, if s1 is the hypotenuse, then we determine
    if s1 = square root(s2^2 + s3^2) to determine if the triangle is right or not.  */
 	
 
import java.util.*;		// for Scanner

public class RightTriangle3
{
	public static void main(String[] args)
	{
		int p1x, p1y, p2x, p2y, p3x, p3y;			// the 3 points as cartesian (x,y) coordinates
		double s1, s2, s3;							// given the 3 points, we compute the 3 sides and store them in these doubles
		boolean right;								// used to store whether the triangle is a right triangle or not
		
		Scanner in=new Scanner(System.in);			// For keyboard input
		System.out.print("Input p1x: ");			// prompt the user and input point 1
		p1x=in.nextInt();
		System.out.print("Input p1y: ");
		p1y=in.nextInt();		
			
		System.out.print("Input p2x: ");			// prompt the user and input point 2
		p2x=in.nextInt();			
		System.out.print("Input p2y: ");
		p2y=in.nextInt();			

		System.out.print("Input p3x: ");			// prompt the user and input point 3
		p3x=in.nextInt();			
		System.out.print("Input p3y: ");
		p3y=in.nextInt();			
		
		// compute the length of each side
		s1=computeSide(p1x,p1y,p2x,p2y);			// s1 is the side connecting points 1 & 2
		s2=computeSide(p2x,p2y,p3x,p3y);			// s2 is the side connecting points 2 & 3
		s3=computeSide(p3x,p3y,p1x,p1y);			// s3 is the side connecting points 1 & 3
		
		right=computePythagorean(s1,s2,s3);			// determine if triangle is right triangle or not and output result
		if(right)
			System.out.println("the triangle formed out of these points is a right triangle");
		else System.out.println("the triangle formed out of these points is a not right triangle");
		
		System.exit(0);								// exit program
	}
	
	// This method uses the Euclidean distance formula to compute the distance between two cartesian points.
	// The return value is a double, automatically cast because of the Math.sqrt method.
	public static double computeSide(int x1, int y1, int x2, int y2)
	{
		return Math.sqrt(Math.pow((x1-x2),2)+Math.pow((y1-y2),2));
	}
	
	// This method determines if the 3 lengths passed to it form a right triangle using
	// the Pythagorean theorem.  In this case, assuming s1 is the longest, it is determining
	// if s1^2 = s2^2 + s3^2.  It is doing it by taking the square root of both sides.
	// This method returns a boolean based on the application of the theorem.
	public static boolean computePythagorean(double s1, double s2, double s3)	
	{
		// determine which side is longest first
		if(s1>s2&&s1>s3) return (s1==Math.sqrt(s2*s2+s3*s3));	// s1 is longest
		else if (s2>s1&&s2>s3) return (s2==Math.sqrt(s1*s1+s3*s3));  // s2 is longest
		else return (s3==Math.sqrt(s1*s1+s2*s2));	// s3 is longest
	}
}