Matrix.transformPoint()

var circle:Shape = Shape(addChild(new Shape()));
with(circle.graphics) beginFill(0x00000), drawCircle(0,0,10);

var point:Point = new Point();
var trans:Matrix = new Matrix();
trans.rotate(Math.PI);
trans.scale(.5, .5);
trans.tx = stage.stageWidth / 2;
trans.ty = stage.stageHeight / 2;

addEventListener(Event.ENTER_FRAME, onLoop);

function onLoop(evt:Event):void {
	point.x = mouseX - trans.tx;
	point.y = mouseY - trans.ty;
	
	point = trans.transformPoint(point);
	
	circle.x = point.x;
	circle.y = point.y;
}

If you don’t feel like rolling your own transformations Matrix.transformPoint() is a very powerful method. It simply applies the tranformations of a given matrix to a Point. The above example scales rotates and translates a point which is then used to position a circle Shape.

Matrix.transformPoint() is well suited for creating orbiting behavior:

var circle:Shape = Shape(addChild(new Shape()));
with(circle.graphics) beginFill(0x00000), drawCircle(0,0,10);

var point:Point = new Point(100,0);
var trans:Matrix = new Matrix();
 trans.rotate(.1);
 trans.scale(.99,.99);

addEventListener(Event.ENTER_FRAME, onLoop);

function onLoop(evt:Event):void {
	 
      point = trans.transformPoint(point);
	 
      circle.x = point.x + stage.stageWidth / 2;
      circle.y = point.y + stage.stageHeight / 2;
}

This code will cause the circle Shape to move in a spiral formation.