Develop an implementation of your Rectangle API from EXERCISE 3.2.1 that represents rectan...

Develop an implementation of your Rectangle API from EXERCISE 3.2.1 that represents rectangles with the x- and y-coordinates of their lower-left and upper-right corners. Do not change the API.

EXERCISE 3.2.1

Consider the following data-type implementation for axis-aligned rectangles, which represents each rectangle with the coordinates of its center point and its width and height:

public class Rectangle{   private final double x, y;   // center of rectangle   private final double width;  // width of rectangle   private final double height; // height of rectangle   public Rectangle(double x0, double y0, double w, double h)   {      x = x0;      y = y0;      width = w;      height = h;   }   public double area()   { return width * height; }   public double perimeter()   { /* Compute perimeter. */ }   public boolean intersects(Rectangle b)   { /* Does this rectangle intersect b? */ }   public boolean contains(Rectangle b)   { /* Is b inside this rectangle? */ }   public void draw(Rectangle b)   { /* Draw rectangle on standard drawing. */ }}

Write an API for this class, and fill in the code for perimeter(), intersects(), and contains(). Note: Consider two rectangles to intersect if they share one or more common points (improper intersections). For example, a.intersects(a) and a.contains(a) are both true.