Find Middle of line

I need to find the middle of this line and follow it.

When I move the mouse I want an item to follow along the center of the line that corresponds with the mouses x. I dont care if this is the whole stage or just when the mouse is inside the line itself.

But it needs to give leeway from the center, so that you dont have to trace it exactly.


Any help is appreciated, thanks

package 
{
	import flash.display.*;
	import flash.events.Event;
	import flash.events.MouseEvent;
	import flash.text.TextField;
	
 
	public class Main extends Sprite 
	{
		
		public function Main():void 
		{
			
			
					
 
				var lineDrawing:Sprite = new Sprite();
				lineDrawing.graphics.lineStyle(80, 0x0000FF);
				lineDrawing.graphics.moveTo(0,0); 
				lineDrawing.graphics.lineTo(350, 600);
				lineDrawing.graphics.lineTo(600, 400);
				lineDrawing.addEventListener(MouseEvent.MOUSE_MOVE, mse_over);
				addChild(lineDrawing);
				 
 
		//		var square:Sprite = new Sprite();
		//		addChild(square);
			//	square.graphics.lineStyle(3,0x00ff00);
				//square.graphics.beginFill(0x00ff00);
				//square.graphics.drawRect(10,45,75,10);
				//square.graphics.endFill();
				
				var label:TextField = new TextField();
				addChild(label);
				
				
				function mse_over(event:MouseEvent):void
					{
							label.autoSize = "left";
							label.text = mouseX.toString() + "," + mouseY.toString();
							//label.x = ;
							//label.y = "";
							square.x = 5 + mouseX;
							square.y = mouseY - 66;
					}
	}
}}

Select allOpen in new window