public class Point{

    // doubles are floating point numbers too. Specification merely states that
    // the inputs are floating point numbers, hence double is chosen
    // =======================================================================
    double x, y;
    // constructor
    Point(double x,double y){
      this.x = x;
      this.y = y;
    }

    // midPoint method takes in a point relative to current point,
    //  and returns midpoint of the line b/w the two:
    public Point midPoint(Point otherPoint){
        double newX = (this.x + otherPoint.x) / 2;
        double newY = (this.y + otherPoint.y) / 2;
        return new Point(newX, newY);
    }

    public double distanceTo(Point otherPoint){
        double dx = -(this.x - otherPoint.x);
        double dy = -(this.y - otherPoint.y);
        return Math.sqrt((dx * dx) + (dy * dy));
    }
    public double angleTo(Point otherPoint){
        // the - factor is to ensure left-side of PQ
        double dx =  otherPoint.x - this.x;
        double dy =  otherPoint.y - this.y;
        return Math.atan2(dy, dx);
    }


    public Point moveTo(double angle, double d){
        return new Point(this.x + (d * Math.cos(angle)),
                         this.y + (d * Math.sin(angle)));
    }
   @Override
    public boolean equals(Object obj) {
        if(this== obj) {
            return true;
        } else if (obj instanceof Point) {
        Point p = (Point) obj;
        return Math.abs(this.x - p.x) < 1E-15 &&
                Math.abs(this.y - p.y) < 1E-15;
        } else{
            return false;
        }
    }


    // toString method:
    @Override
    public String toString(){
        return "point (" + String.format("%.3f", this.x)
                          + ", " + String.format("%.3f", this.y) + ")";
    }


}