split a line based on a user click

splitline.cs

var shape = (Polyline)row["Shape"];

var point = (MapPoint)GeometryEngine.Instance.Project(userClickGeometry, shape.SpatialReference);
var proximity = GeometryEngine.Instance.NearestPoint(shape, point);
var distance = proximity.Distance * 2;

var vertices = new List<Coordinate2D>
{
    new Coordinate2D(point),
    new Coordinate2D(proximity.Point),
};

var polyline = PolylineBuilder.CreatePolyline(vertices, point.SpatialReference);

var extension = GeometryEngine.Instance.MovePointAlongLine(polyline, distance, false, 0,
    SegmentExtension.ExtendEmbedded);

vertices.Add(new Coordinate2D(extension));

polyline = PolylineBuilder.CreatePolyline(vertices, point.SpatialReference);

var parts = GeometryEngine.Instance.Cut(shape, polyline);
var totalLength = shape.Length;
var polylines = parts.Select(x => (Polyline)x).ToArray();