#include <iostream>
#include <cmath>   //for the functions sqrt, atan2, and abs
#include "point.h"
using namespace std;

point::point(double initial_x, double initial_y)
	: x {initial_x}, y {initial_y}
{
}

point::point()
	: x {0}, y {0}
{
}

double point::r() const   //distance to origin
{
	return sqrt(x * x + y * y);
}

double point::theta() const
{
	return atan2(y, x);   //two-argument arctangent
}

void point::print() const
{
	cout << "(" << x << ", " << y << ")";
}

double distance(const point& A, const point& B)
{
	const double dx {A.x - B.x};
	const double dy {A.y - B.y};
	return sqrt(dx * dx + dy * dy);
}

double area(const point& A, const point& B, const point& C)
{
	return abs(A.x * (B.y - C.y) +
		   B.x * (C.y - A.y) +
		   C.x * (A.y - B.y)) / 2.0;
}