(Geometry: find the bounding rectangle) A bounding rectangle is the minimum rectangle that...

(Geometry: find the bounding rectangle) A bounding rectangle is the minimum rectangle that encloses a set of points in a two-dimensional plane, as shown in Figured. Write a function that returns a bounding rectangle for a set of points in a two-dimensional plane, as follows:

const int SIZE = 2 ;
Rectang1e2D getRectang1e(const double points[][SIZE]);

The Rectang1e2D class is defined in Programming Exercise. Write a test program that prompts the user to enter five points and displays the bounding rectangle’s center, width, and height. Here is a sample run:

Figured

Programming Exercise. (Geometry: The Rectangle2D class) Define the Rectangle2D class that contains:

■ Two double data fields named x and y that specify the center of the rectan­gle with constant get functions and set functions. (Assume that the rectangle sides are parallel to x- or y- axes.)

■ The double data fields width and height with constant get functions and set functions.

■ A no-arg constructor that creates a default rectangle with (0 , 0) for (x , y) and 1 for both width and height.

■ A constructor that creates a rectangle with the specified x , y , width , and height.

■ A constant function getArea() that returns the area of the rectangle.

■ A constant function getPerimeter() that returns the perimeter of the rectangle.

■ A constant function contains(double x, double y) that returns true if the specified point (x , y) is inside this rectangle. See Figurea.

■ A constant function contains(const Rectangle2D &r) that returns true if the specified rectangle is inside this rectangle. See Figureb.

■ A constant function overlaps(const Rectangle2D &r) that returns true if the specified rectangle overlaps with this rectangle. See Figurec.

Figure (a) A point is inside the rectangle. (b) A rectangle is inside another rectangle.

(c) A rectangle overlaps another rectangle. (d) Points are enclosed inside a rectangle.

Draw the UML diagram for the class. Implement the class. Write a test program that creates three Rectangle2D objects r1(2, 2, 5.5, 4.9) , r2(4,5, 10.5, 3.2)) , and r3(3, 5, 2.3, 5.4) , and displays r1 ’s area and perimeter, and displays the result of r1.contains(3, 3) , r1.contains(r2) , and r1. overlaps(r3).