Assuming your desired reference point on your line is the first x/y in points[], you can get the line's position relative to the top-left canvas corner like this:
Save the original XY of that reference point as new properties on the line
Listen to the dragmove event and add that original XY back to the current getX/getY
Results: position of the line relative to canvas [0,0]
Alternatively, if you wanted the position of your line's bounding box, you must first iterate through each point and fetch the line's top-left most XY.
Here's code and a Fiddle: http://jsfiddle.net/m1erickson/jELRL/
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>Prototype</title>
<script type="text/javascript" src="http://code.jquery.com/jquery.min.js"></script>
<script src="http://d3lp1msu2r81bx.cloudfront.net/kjs/js/lib/kinetic-v4.7.2.min.js"></script>
<style>
body{padding:20px;}
#container{
border:solid 1px #ccc;
margin-top: 10px;
width:350px;
height:350px;
}
</style>
<script>
$(function(){
var stage = new Kinetic.Stage({
container: 'container',
width: 350,
height: 350
});
var layer = new Kinetic.Layer();
stage.add(layer);
var $results=$("#results");
var line = new Kinetic.Line({
points: [121, 27, 165, 99],
stroke: '#ff0000',
strokeWidth: 10,
draggable: true
});
var point=line.getPoints()[0];
line.originalX=point.x;
line.originalY=point.y;
line.on("dragmove",function(){
$results((this.getX()+this.originalX)+"/"+(this.getY()+this.originalY));
});
layer.add(line);
layer.draw();
}); // end $(function(){});
</script>
</head>
<body>
<p id="results">Results</p>
<div id="container"></div>
</body>
</html>