#include <cmath>   //for sqrt
#include "point.h"
using namespace std;

const point point_origin;   //give arguments 0.0, 0.0 to constructor

//Return the distance between this point and the origin.

double point::dist() const
{
	const double dx = point_origin.x - x;
	const double dy = point_origin.y - y;

	return sqrt(dx * dx + dy * dy);               //Pythagorean theorem
}

//Return the distance between this point and another.

double point::dist(const point& another) const
{
	const double dx = another.x - x;
	const double dy = another.y - y;

	return sqrt(dx * dx + dy * dy);
}

//Return the area of the triangle whose vertices are points *this, B, and C.

double point::area(const point& B, const point& C) const
{
	return abs(x * B.y + B.x * C.y + C.x * y
		 - y * B.x - B.y * C.x - C.y * x) / 2;
}