// package classes;

public class Rectangle {

	int x;
	int y;
	int width;
	int height;
	Point point;

//initialize the constructor with point, width and height
	public Rectangle(Point p, int width, int height) {

		this.point = p;
		this.width = width;
		this.height = height;
	}

	public Rectangle(int x, int y, int width, int height) {
		this.x = x;
		this.y = y;
		this.width = width;
		this.height = height;

	}

     // this method returns the intersection of two rectangles
    public Rectangle intersection(Rectangle rect) {
		if (this.x + this.width < rect.x || rect.x + rect.width < this.x
				|| this.y + this.height < rect.y || rect.y + rect.height < this.y)
			return null;

		int x1 = Math.max(this.x, rect.x);
		int y1 = Math.max(this.y, rect.y);
		int x2 = Math.min(this.x + this.width, rect.x + rect.width);
		int y2 = Math.min(this.y + this.height, rect.y + rect.height);

		return new Rectangle(x1, y1, x2 - x1, y2 - y1);
	}

   public boolean contains(int x, int y) {
		return this.x <= x && x <= this.x + width && this.y <= y && y <= this.y + height;
	}

	public boolean contains(Point p) {
		return contains(p.getX(), p.getY());
	}

	public int getX() {
		return x;
	}

	public void setX(int x) {
		this.x = x;
	}

	public int getY() {
		return y;
	}

	public void setY(int y) {
		this.y = y;
	}

	public int getWidth() {
		return width;
	}

	public void setWidth(int width) {
		this.width = width;
	}

	public int getHeight() {
		return height;
	}

	public void setHeight(int height) {
		this.height = height;
	}

	@Override
	public String toString() {

		return "[Rectangle x = " + this.x + ", y = " + this.y + ", width = " + width + ", height =  " + height + "]";

	}

	public static void main(String[] args) {

		Rectangle rec = new Rectangle(4, 6, 8, 5);
		Rectangle rec1 = new Rectangle(8, 5, 7, 5);

		System.out.println("New Rectangle formed: " + rec.intersection(rec1));
	

	}

}

Output:

New Rectangle formed: [Rectangle x = 8, y = 6, width = 4, height =  4]