public void RemovePoint( 
   int index
)

// 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();
  }
});


// or use the builderEx constructors = don't need to run on the MCT.
MultipointBuilderEx builderEx = new MultipointBuilderEx(multipoint);
// remove the first point
builderEx.RemovePoint(0);
// modify the coordinates of the last point
var ptEx = builderEx.GetPoint(builderEx.PointCount - 1);
builderEx.RemovePoint(builderEx.PointCount - 1);

var newPtEx = MapPointBuilder.CreateMapPoint(ptEx.X + 1.0, ptEx.Y + 2.0);
builderEx.AddPoint(newPtEx);
Multipoint modifiedMultiPointEx = builderEx.ToGeometry() as Multipoint;