public void RemovePoint( 
   int pointIndex
)

// Builder constructors need to run on the MCT.
ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
{
  // assume a multiPoint has been built from 4 points
  // the modified multiPoint will have the first point removed and the last point moved

  using (MultipointBuilder mpb = new MultipointBuilder(multipoint))
  {
    // remove the first point
    mpb.RemovePoint(0);

    // modify the coordinates of the last point
    MapPoint pt = mpb.GetMapPoint(mpb.PointCount - 1);
    mpb.RemovePoint(mpb.PointCount - 1);

    MapPoint newPt = MapPointBuilder.CreateMapPoint(pt.X + 1.0, pt.Y + 2.0);
    mpb.Add(newPt);

    Multipoint modifiedMultiPoint = mpb.ToGeometry();
  }
});