Using the rest api, I need to return a polyline feature and find the midpoint of the line. It does not appear the api currently has any methods to return centroid or midpoints.
You can also calculate the mid point at client side, see this LinearReferencing sample using the Silverlight/WPF API (midpoint is a particular case that you can get by: var midPoint = line.LinearPosition(line.Length()/2); )