Finding a specific point on a rendered line

Consider the following class.
package com.somemythicalpackage
import java.awt.* ;
import java.awt.event.* ;
import javax.swing.* ;
public class DrawrALine extends JPanel implements MouseListener{
     private Point origin, terminus ;
     public DrawrALine(){
          super() ;
     public DrawrALine(Point _origin, Point _terminus){
          this() ;
          origin = _origin ;
          terminus = _terminus ;
          addMouseListener(this) ;
          render() ;
     private void render(){
          if(origin == null || terminus == null){
               return ;
          setBounds(origin.x, origin.y, (terminus.x - origin.x), (terminus.y - origin.y)) ;
     public void paintComponent(Graphics _g){
          _g.setColor(Color.BLACK) ;
          _g.drawLine(0, 0, getWidth(), getHeight()) ;
     public void mouseClicked(MouseEvent e){
          Point p = e.getPoint() ;
               Here's the question, how to determine if the Point p
               is on the line defined as being from (0:0) - (width : height)?
               Reason being that I want the program to respond when
               and only when the user clicks on the line, not if they
               click elsewhere within the bounds defined by the JPanel.
     public void mouseEntered(MouseEvent e){}
     public void mouseExited(MouseEvent e){}
     public void mousePressed(MouseEvent e){}
     public void mouseReleased(MouseEvent e){}
}In the actual application I am using this renderer class to draw lines semantically connecting objects in a graphical workspace. However, the type of connection has to be determined by the user. To that end ultimately I want to respond when the user double clicks on the line. Catching the double click is a trivial matter, but the struggle I am having is how to detemine if the user actually clicked on the line. The mouseClicked event fires anytime a mouse is clicked inside the bounds of the JPanel, and that doesn't accomplish what I need for two reasons. First, some of the bounding rectangles overlap so the user would be double clicking on the wrong connection. Secondly, it's sloppy to have the application respond because the user clicked in the same zipcode as the line.
(Right now I would give a lot for a 10th grade geometry book)
Regards, and thanks in advance for suggestions.
PS

Here's another way:
import java.awt.*;
import java.awt.geom.*;
import java.awt.event.*;
import javax.swing.*;
public class DrawLine extends Line2D {
   private String id;
   private Point2D p1, p2;
   public DrawLine(String _id, Point2D _p1, Point2D _p2) {
      super();
      id = _id;
      p1 = _p1;
      p2 = _p2;
      //addMouseListener(this);
      //render();
   public String getId() {
      return id;
   /* (non-Javadoc)
    * @see java.awt.geom.Line2D#getX1()
   public double getX1() {
      // TODO Auto-generated method stub
      return p1.getX();
   /* (non-Javadoc)
    * @see java.awt.geom.Line2D#getY1()
   public double getY1() {
      // TODO Auto-generated method stub
      return p1.getY();
   /* (non-Javadoc)
    * @see java.awt.geom.Line2D#getP1()
   public Point2D getP1() {
      // TODO Auto-generated method stub
      return p1;
   /* (non-Javadoc)
    * @see java.awt.geom.Line2D#getX2()
   public double getX2() {
      // TODO Auto-generated method stub
      return p2.getX();
   /* (non-Javadoc)
    * @see java.awt.geom.Line2D#getY2()
   public double getY2() {
      // TODO Auto-generated method stub
      return p2.getY();
   /* (non-Javadoc)
    * @see java.awt.geom.Line2D#getP2()
   public Point2D getP2() {
      // TODO Auto-generated method stub
      return p2;
   /* (non-Javadoc)
    * @see java.awt.geom.Line2D#setLine(double, double, double, double)
   public void setLine(double arg0, double arg1, double arg2, double arg3) {
      // TODO Auto-generated method stub
   /* (non-Javadoc)
    * @see java.awt.Shape#getBounds2D()
   public Rectangle2D getBounds2D() {
     return new Rectangle2D.Double(getX1(), getY1(), getX2() - getX1(),
                                                      getY2() - getY1());
   public static void main(String[] args) {
      JFrame f = new JFrame();
      final DrawLine[] lines = new DrawLine[10];
      Point p1, p2;
      for (int i = 0; i < lines.length; i++) {
         p1 = new Point(i * 10, i * 30);
         p2 = new Point(600 - (i * 10), 400 - (i * 30));
         lines[i] = new DrawLine("l" + i, p1, p2);
      LinePanel panel = new LinePanel(lines);
      panel.addMouseListener(new MouseAdapter() {
         public void mouseClicked(MouseEvent e) {
            Point p = e.getPoint();
            System.out.println("clicked at "+p);
            Rectangle2D.Double prect = new Rectangle2D.Double((double)p.x, (double)p.y,
                                                    (double)2, (double)2);
            for (int i=0; i<lines.length; i++) {                                        
               if (lines.intersects(prect)) {
System.out.println("clicked on line " + lines[i].getId());
f.getContentPane().add(panel, BorderLayout.CENTER);
f.setSize(600, 400);
f.setVisible(true);
class LinePanel extends JPanel {
private Line2D[] lines;
public LinePanel(Line2D[] _lines) {
super(null);
this.lines = _lines;
public void paintComponent(Graphics g) {
super.paintComponent(g);
Graphics2D g2 = (Graphics2D)g;
for (int i=0; i<lines.length; i++) {                                        
g2.draw(lines[i]);
Hope this helped,
Regards.

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