Question is from here:

Consider a list of four points on a plane; the points have integral coordinates, and their order is irrelevant. The four points determine a square if the distances between them are all equal, and the lengths of the two diagonals are also equal. For instance, the following lists are all squares:

(0,0), (0,1), (1,1), (1,0) — the unit square
(0,0), (2,1), (3,-1), (1, -2) — square not aligned to axis
(0,0), (1,1), (0,1), (1,0) — unit square, in different order

And the following lists do not represent squares:

(0,0), (0,2), (3,2), (3,0) — rectangle
(0,0), (3,4), (8,4), (5,0) — rhombus
(0,0), (0,0), (1,1), (0,0) — degenerate
(0,0), (0,0), (1,0), (0,1) — degenerate

The degenerate square that consists of four repetitions of a single point may be considered either square, or not.

Your task is to write a function that determines if four input points determine a square.

Solution:

public class Four_Points_Determine_A_Square {
	public static void main(String[] args) {
		System.out.println(isSquare(new Pair(0, 0), new Pair(0, 1),
				new Pair(1, 1), new Pair(1, 0)));
		System.out.println(isSquare(new Pair(0, 0), new Pair(2, 1),
				new Pair(3, -1), new Pair(1, -2)));
		System.out.println(isSquare(new Pair(0, 0), new Pair(1, 1),
				new Pair(0, 1), new Pair(1, 0)));
		System.out.println(isSquare(new Pair(0, 0), new Pair(0, 2),
				new Pair(3, 2), new Pair(3, 0)));
		System.out.println(isSquare(new Pair(0, 0), new Pair(3, 4),
				new Pair(8, 4), new Pair(5, 0)));
	}

	private static boolean isSquare(Pair p1, Pair p2, Pair p3, Pair p4){
		double dis1, dis2, dis3;
		//calculating distance - reference is p1
		dis1 = Math.pow((p1.returnX() - p2.returnX()), 2) +
				Math.pow((p1.returnY() - p2.returnY()), 2);
		dis2 = Math.pow((p1.returnX() - p3.returnX()), 2) +
				Math.pow((p1.returnY() - p3.returnY()), 2);
		dis3 = Math.pow((p1.returnX() - p4.returnX()), 2) +
				Math.pow((p1.returnY() - p4.returnY()), 2);
		//two smaller distances are side and
		//largest is the diagonal
		double[] points = {dis1, dis2, dis3};
		java.util.Arrays.sort(points);
		//two smaller distances are side
		//and must be equal
		if(points[0] != points[1])
			return false;
		//Pythagorean theorem: sum of square of sides
		//is equal to square of diagonal
		if(points[0] + points[1] != points[2])
			return false;
		return true;
	}
	//inner class
	static class Pair{
		private int x;
		private int y;

		public Pair(int x, int y){
			this.x = x;
			this.y = y;
		}
		public void setX(int x){
			this.x = x;
		}
		public int returnX(){
			return x;
		}
		public void setY(int y){
			this.y = y;
		}
		public int returnY(){
			return y;
		}
	}
}

Output:

true
true
true
false
false