#include <iostream>
#include <cmath>
using namespace std;

class point
{
friend class triangle;
friend bool point_eq(point & a, point & b);
public:
    point();
    point(double x, double y);
    double x() const;
    double y() const;
    double distance(point & p) const;
private:
    double my_x;
    double my_y;
};

point::point()
:my_x(0), my_y(0)
{
}

point::point(double x, double y)
:my_x(x), my_y(y)
{
}

double point::x() const
{
    return my_x;
}

double point::y() const
{
    return my_y;
}

double point::distance(point & p) const
{
    return sqrt(pow(my_x-p.my_x,2)+pow(my_y-p.my_y,2));
}

bool point_eq(point & a, point & b)
{
    return ((a.my_x == b.my_x) && (a.my_y == b.my_y));
}

bool operator == (point & a, point & b)
{
    return (a.x() == b.x() && a.y() == b.y());
}

bool operator != (point & a, point & b)
{
    return (a.x() != b.x() || a.y() != b.y());
}

class triangle
{
public:
    triangle();
    triangle(point a, point b, point c);
    point p1();
    point p2();
    point p3();
    double area();
    point center();
    void shift(point v);

private:
    point my_p1;
    point my_p2;
    point my_p3;
};

triangle::triangle()
{
    my_p1 = point(0,0); 
    my_p2 = point(0,0); 
    my_p3 = point(0,0);
}

triangle::triangle(point a, point b, point c)
{
    my_p1 = a;  
    my_p2 = b;  
    my_p3 = c;
}

point triangle::p1()
{
    return my_p1;
}

point triangle::p2()
{
    return my_p2;
}

point triangle::p3()
{
    return my_p3;
}

double triangle::area()
{
    double a,b,c,s,Area;
    a = my_p1.distance(my_p2);
    b = my_p2.distance(my_p3);
    c = my_p3.distance(my_p1);
    s = (a+b+c)/2;
    Area = sqrt(s*(s-a)*(s-b)*(s-c));
    return Area;
}

point triangle::center()
{
    double x,y;
    x = (my_p1.my_x+my_p2.my_x+my_p3.my_x)/3.0;
    y = (my_p1.my_y+my_p2.my_y+my_p3.my_y)/3.0;
    return point(x,y);
}

void triangle::shift(point v)
{
    my_p1.my_x += v.x();
    my_p1.my_y += v.y();
    my_p2.my_x += v.x();
    my_p2.my_y += v.y();
    my_p3.my_x += v.x();
    my_p3.my_y += v.y();
}

void main()
{
    point a, b(3,4),c(3,0),v(1,1);

    if (a == b || a == c || b == c)
    {
        cout << "The three points can't form a triangle!!\n";
        return;
    }

    cout << "The lengthes of the three sides of the triangle are: "
         << b.distance(a) << ", " << b.distance(c)
         << ", " << a.distance(c) << ".\n\n";

    triangle t(a,b,c);

    cout << "a:(" << a.x() << "," << a.y() << ") ";
    cout << "b:(" << b.x() << "," << b.y() << ") ";
    cout << "c:(" << c.x() << "," << c.y() << ")\n";
    cout << "The center of triangle is (" << t.center().x()
         << "," << t.center().y() << ").\n";
    cout << "The area of the triangle is " << t.area() << endl << endl;
 
    if (v != point())
    {
        t.shift(v);
        cout << "After shift" << endl;
        cout << "a:(" << t.p1().x() << "," << t.p1().y() << ") ";
        cout << "b:(" << t.p2().x() << "," << t.p2().y() << ") ";
        cout << "c:(" << t.p3().x() << "," << t.p3().y() << ")\n";
        cout << "The center of triangle is (" << t.center().x()
             << "," << t.center().y() << ").\n";
        cout << "The area of the triangle is " << t.area() << endl << endl;
    }
}