theBoard: movie clip, the same size as the stage.

import flash.display.Shape;
       import flash.events.MouseEvent;
       import flash.geom.Point;
       import flash.events.Event;

 stop();
         var myShape:Shape = new Shape();
         theBoard.addChild(myShape);
   
         stage.addEventListener(MouseEvent.MOUSE_DOWN, startToDraw);
         stage.addEventListener(MouseEvent.MOUSE_UP, stopDrawing);
         stage.addEventListener(Event.ENTER_FRAME, drawTheLine);
   
         var coordinates:Array;
         var i:int =0;
         var beginToDraw :Boolean = false;
   
         function startToDraw(e:MouseEvent){
             coordinates = new Array();
             coordinates.push(new Point(mouseX, mouseY));
             myShape.graphics.lineStyle(4, 0xffffff);
             //myShape.graphics.moveTo(mouseX, mouseY);
             beginToDraw = true;
         }
   
         function drawTheLine(e:Event){
             if(beginToDraw == true){
                coordinates.push(new Point(mouseX, mouseY));
                for(i = 0; i <coordinates.length-1; i++){
                     myShape.graphics.moveTo(coordinates[i].x, coordinates[i].y);
                     myShape.graphics.lineTo(coordinates[i+1].x, coordinates[i+1].y);
                     trace(coordinates[i].x + ",  " + coordinates[i].y);
                }
             }
         }
   
         function stopDrawing(e:MouseEvent){
            beginToDraw = false;
            myShape.graphics.clear();
         }