If you're just multiplying by 20 to get the translated point, I really don't recommend using a HashMap to do that. Instead, just use a method.
Point getTransformedPoint(Point p)
return new Point(p.x * 20, p.y * 20);
Something like that.
I also wouldn't extend Rectangle. Instead if you want to use Rectangle, store one in the class's fields. It doesn't make sense to extend Rectangle because your classes aren't actually shapes.
You would do something like this:
public class MyClass
private Rectangle bounds;
public Rectangle getBounds()
public boolean intersects(MyClass mc)