public virtual MapPoint StartPoint {get; set;}

{
  MapPoint startPt = MapPointBuilderEx.CreateMapPoint(1.0, 1.0);
  MapPoint endPt = MapPointBuilderEx.CreateMapPoint(2.0, 1.0);
  // 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);
}