public MapPoint StartPoint {get;}

{
  // Method 1: Get the start point of the polyline by converting the polyline 
  //    into a collection of points and getting the first point

  // sketchGeometry is a Polyline
  // get the sketch as a point collection
  Geometry sketchGeometry = polyline; // for example
  var pointCol = ((Multipart)sketchGeometry).Points;
  // Get the start point of the line
  var firstPoint = pointCol[0];

  // Method 2: Convert polyline into a collection of line segments 
  //   and get the "StartPoint" of the first line segment.
  var polylineGeom = sketchGeometry as ArcGIS.Core.Geometry.Polyline;
  var polyLineParts = polylineGeom.Parts;

  ReadOnlySegmentCollection polylineSegments = polyLineParts.First();

  //get the first segment as a LineSegment
  var firsLineSegment = polylineSegments.First() as LineSegment;

  //Now get the start Point
  var startPointOfSegment = firsLineSegment.StartPoint;
}

{
  // retrieve the bezier curve's control points
  CubicBezierSegment cb = CubicBezierBuilderEx.CreateCubicBezierSegment(bezierSegment);
  MapPoint startPt = cb.StartPoint;
  Coordinate2D ctrlPt1 = cb.ControlPoint1;
  Coordinate2D ctrlPt2 = cb.ControlPoint2;
  MapPoint endPt = cb.EndPoint;

  bool isCurve = cb.IsCurve;
  double len = cb.Length;
}