public ReadOnlyPointCollection Points {get;}

{
  // get the points as a readonly Collection
  //Refer to the initialization region for polyline creation
  ReadOnlyPointCollection pts = polyline.Points;
  int numPts = polyline.PointCount;

  // OR   get an enumeration of the points
  IEnumerator<MapPoint> enumPts = polyline.Points.GetEnumerator();

  // OR   get the point coordinates as a readonly list of Coordinate2D
  IReadOnlyList<Coordinate2D> coordinates = polyline.Copy2DCoordinatesToList();

  // OR   get the point coordinates as a readonly list of Coordinate3D
  IReadOnlyList<Coordinate3D> coordinates3D = polyline.Copy3DCoordinatesToList();

  // OR   get a subset of the collection as Coordinate2D using preallocated memory

  IList<Coordinate2D> coordinate2Ds = new List<Coordinate2D>(10);   // allocate some space
  ICollection<Coordinate2D> subsetCoordinates2D = coordinate2Ds;    // assign
  pts.Copy2DCoordinatesToList(1, 2, ref subsetCoordinates2D);       // copy 2 elements from index 1 into the allocated list
                                                                    // coordinate2Ds.Count = 2
                                                                    // do something with the coordinate2Ds

  // without allocating more space, obtain a different set of coordinates
  pts.Copy2DCoordinatesToList(5, 9, ref subsetCoordinates2D);       // copy 9 elements from index 5 into the allocated list
                                                                    // coordinate2Ds.Count = 9


  // OR   get a subset of the collection as Coordinate3D using preallocated memory

  IList<Coordinate3D> coordinate3Ds = new List<Coordinate3D>(15);   // allocate some space
  ICollection<Coordinate3D> subsetCoordinates3D = coordinate3Ds;    // assign
  pts.Copy3DCoordinatesToList(3, 5, ref subsetCoordinates3D);       // copy 5 elements from index 3 into the allocated list
                                                                    // coordinate3Ds.Count = 5


  // OR   get a subset of the collection as MapPoint using preallocated memory

  IList<MapPoint> mapPoints = new List<MapPoint>(7);   // allocate some space
  ICollection<MapPoint> subsetMapPoint = mapPoints;    // assign
  pts.CopyPointsToList(1, 4, ref subsetMapPoint);      // copy 4 elements from index 1 into the allocated list
                                                       // mapPoints.Count = 4
}

{
  // 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;
}

{
  // get the points as a readonly Collection
  ReadOnlyPointCollection pts = polygon.Points;

  // get an enumeration of the points
  IEnumerator<MapPoint> enumPts = polygon.Points.GetEnumerator();

  // get the point coordinates as a readonly list of Coordinate2D
  IReadOnlyList<Coordinate2D> coordinates = polygon.Copy2DCoordinatesToList();

  // get the point coordinates as a readonly list of Coordinate3D
  IReadOnlyList<Coordinate3D> coordinates3D = polygon.Copy3DCoordinatesToList();
}