$/**$

This class represents "immutable" rectangles in the plane.

We say that an object is "immutable" if you cannot change

it after it is created.

Whenever you wish to modify some aspect of a Rectangle, you

actually get a new Rectangle in which the modification has

been done.

The fields of this class are both private and final. Private

means they cannot be seen by any code outside of this class.

The final modifier means that the values of those variables

cannot be change by any code, even code in this class $($except

that they can be initialized by the constructor$).$

$*/$

public class Rectangle

$\{$

private final double x; $//($x$,$y$)$ is the upper left$-$hand corner of this rectangle

private final double y;

private final double width;

private final double height;

$/**$

@param x x$-$coordinate of this Rectangle's upper left$-$hand corner

@param y y$-$coordinate of this Rectangle's upper left$-$hand corner

@param width width of this Rectangle, must be strictly positive

@param height height of this Rectangle, must be strictly positive

@throws IllegalArgumentException when width is not strictly positive

@throws IllegalArgumentException when height is not strictly positive

$*/$

public Rectangle$($double x$,$ double y$,$ double width, double height$)$

$\{$

$//$ implementation

$\}$

$/**$

@return the x$-$coordinate of this Rectangle's upper left$-$hand corner

$*/$

public double getX$()$

$\{$

$//$ implementation

$\}$

$/**$

@return the y$-$coordinate of this Rectangle's upper left$-$hand corner

$*/$

public double getY$()$

$\{$

$//$ implementation

$\}$

$/**$

@return the value of this Rectangle's width

$*/$

public double getWidth$()$

$\{$

$//$ implementation

$\}$

$/**$

@return the value of this Rectangle's height

$*/$

public double getHeight$()$

$\{$

$//$ implementation

$\}$

$/**$

@return the value of this Rectangle's area

$*/$

public double getArea$()$

$\{$

$//$ implementation

$\}$

$/**$

@return the value of this Rectangle's perimeter

$*/$

public double getPerimeter$()$

$\{$

$//$ implementation

$\}$

$/**$

Return a Rectangle object that has the same upper left$-$hand

corner and height as this Rectangle but with the given width.

@param width the width for the new rectangle

@return a Rectangle with the given width and the same upper left$-$hand corner and height as this rectangle

$*/$

public Rectangle setWidth$($double width$)$

$\{$

$//$ implementation

$\}$

$/**$

Return a Rectangle object that has the same upper left$-$hand

corner and width as this Rectangle but with the given height.

@param height the height for the new rectangle

@return a Rectangle with the given height and the same upper left$-$hand corner and width as this rectangle

$*/$

public Rectangle setHeight$($double height$)$

$\{$

$//$ implementation

$\}$

$/**$

Return a Rectangle object that has the same width and height

as this Rectangle but the new Rectangle should have its upper

left$-$hand corner at the given x and y values.

@param x x$-$coordinate for the new Rectangle's upper left$-$hand corner

@param y y$-$coordinate for the new Rectangle's upper left$-$hand corner

@return a Rectangle with the same dimensions but a different upper left$-$hand corner

$*/$

public Rectangle moveTo$($double x$,$ double y$)$

$\{$

$//$ implementation

$\}$

$/**$

Return a Rectangle object that has the same width and height

as this Rectangle but the new Rectangle should have its upper

left$-$hand corner translated from where this Rectangle's upper

left$-$hand corner is$.$

@param dx amount by which to change the x$-$coordinate from this Rectangle

@param dy amount by which to change the y$-$coordinate from this Rectangle

@return a Rectangle with the same dimensions but a different upper left$-$hand corner

$*/$

public Rectangle translateBy$($double dx$,$ double dy$)$

$\{$

$//$ implementation

$\}$

$/**$

Return a Rectangle object that has the same upper left$-$hand

corner as this Rectangle, but the new Rectangle should have

the width and height from this Rectangle flipped.

@return a Rectangle with the same upper left$-$hand corner but with the dimensions flipped

$*/$

public Rectangle flip$()$

$\{$

$//$ implementation

$\}$

$/**$

Return a Rectangle object with the same upper left$-$hand

corner as this Rectangle, a width that is the maximum

of the widths from the two input Rectangles, and with

a height that is the maximum of the heights from the

two input Rectangles.

@param r$1$ the first input Rectangle

@param r$2$ the second input Rectangle

@ret