//Note this shouldn't be of type object, I'm just showing that it is an object
Object myRectangle;
 
 
public void mouseDragged(MouseEvent e){
Object source= e.getSource();
 
if (source == myRectangle){
myRectangle.setColor(whatever.GREEN);
//call some repaint method here
}
 
}

import java.awt.Color;
import java.awt.Graphics;
import java.awt.Point;
import java.awt.event.MouseEvent;
import java.awt.event.MouseMotionListener;
import javax.swing.JApplet;
import javax.swing.JPanel;
 
public class PaintApplet extends JApplet {
 
    public void init() {
        getContentPane().add(new CanvasPanel());
    }
 
    class CanvasPanel extends JPanel implements MouseMotionListener{
        Color backColor = Color.WHITE;
        Color foreColor = Color.BLUE;
 
        Point p0 = new Point(0,0);
        Point p1 = new Point(0,0);
 
        public CanvasPanel(){
            super();
            addMouseMotionListener(this);
        }
 
        @Override
        protected void paintComponent(Graphics g) {
            g.setColor(backColor);
            g.fillRect(0, 0, getWidth(), getHeight());
            g.setColor(foreColor);
            g.drawLine(p0.x, p0.y, p1.x, p1.y);
        }
 
        public void mouseDragged(MouseEvent e) {
            p1.x = e.getX();
            p1.y = e.getY();
            repaint();
        }
 
        public void mouseMoved(MouseEvent e) {
            // nothing here - just want drag operations
        }
    }
}