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

point::point(double init_x, double init_y)
	: x {init_x}, y {init_y}
{
}

point::point() //The default constructor puts the origin into the newborn point.
	: x {0.0}, y {0.0}
{
}

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

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

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

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

bool equals(const point& A, const point& B)  //true if at same coordinates
{
	return A.x == B.X && A.y == B.y;
}

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