public void RemoveGeometry( 
   int index
)

{
  MapPoint point = MapPointBuilderEx.CreateMapPoint(1, 2, SpatialReferences.WebMercator);

  List<Coordinate2D> coords2DToUse = new List<Coordinate2D>()
  {
    new Coordinate2D(0, 0),
    new Coordinate2D(0, 1),
    new Coordinate2D(1, 1),
    new Coordinate2D(1, 0)
  };

  Multipoint multipointNew = MultipointBuilderEx.CreateMultipoint(coords2DToUse, SpatialReferences.WGS84);
  Polyline polylineNew = PolylineBuilderEx.CreatePolyline(coords2DToUse, SpatialReferences.WebMercator);

  GeometryBagBuilderEx builder = new GeometryBagBuilderEx(SpatialReferences.WGS84);

  GeometryBag emptyBag = builder.ToGeometry();
  // emptyBag.IsEmpty = true

  builder.AddGeometry(point);
  // builder.GeometryCount = 1

  GeometryBag geometryBag = builder.ToGeometry();
  // geometryBag.PartCount = 1
  // geometryBag.PointCount = 1
  // geometryBag.IsEmpty = false

  IReadOnlyList<ArcGIS.Core.Geometry.Geometry> geometries = geometryBag.Geometries;
  // geometries.Count = 1
  // geometries[0] is MapPoint with a sr of WGS84

  bool isEqual = geometryBag.IsEqual(emptyBag);   // isEqual = false

  builder.InsertGeometry(0, multipoint);
  geometryBag = builder.ToGeometry();
  // geometryBag.PartCount = 2

  geometries = geometryBag.Geometries;
  // geometries.Count = 2
  // geometries[0] is Multipoint
  // geometries[1] is MapPoint

  builder.AddGeometry(polyline);
  builder.RemoveGeometry(1);
  geometryBag = builder.ToGeometry();
  // geometryBag.PartCount = 2

  geometries = geometryBag.Geometries;
  // geometries.Count = 2
  // geometries[0] is Multipoint
  // geometries[1] is Polyline          
}