public virtual MapPoint StartPoint {get; set;}

// builderEx constructors don't need to run on the MCT
LineBuilderEx lbuilderEx = new LineBuilderEx(lineSegment);
// find the existing coordinates
lbuilderEx.QueryCoords(out startPt, out endPt);

// or use 
//startPt = lbuilderEx.StartPoint;
//endPt = lbuilderEx.EndPoint;

// update the coordinates
lbuilderEx.SetCoords(GeometryEngine.Instance.Move(startPt, 10, 10) as MapPoint, GeometryEngine.Instance.Move(endPt, -10, -10) as MapPoint);

// or use 
//lbuilderEx.StartPoint = GeometryEngine.Instance.Move(startPt, 10, 10) as MapPoint;
//lbuilderEx.EndPoint = GeometryEngine.Instance.Move(endPt, -10, -10) as MapPoint;

LineSegment segment2 = lbuilderEx.ToSegment() as LineSegment;

// retrieve the bezier curve's control points

CubicBezierBuilderEx cbbEx = new CubicBezierBuilderEx(bezierSegment);
MapPoint startPtEx = cbbEx.StartPoint;
Coordinate2D ctrlPt1Ex = cbbEx.ControlPoint1;
Coordinate2D ctrlPt2Ex = cbbEx.ControlPoint2;
MapPoint endPtEx = cbbEx.EndPoint;
     
// or use the QueryCoords method
cbbEx.QueryCoords(out startPtEx, out ctrlPt1Ex, out ctrlPt2Ex, out endPtEx);