Actually - you should get back a line when intersecting 2 lines. My first answer above is incorrect, I will remove it for clarity.
Code should look something like this:
-(void)lineIntersection{
AGSPolyline *lineAB = [AGSPolyline polylineWithPoints:@[AGSPointMakeWGS84(0, 0), AGSPointMakeWGS84(10, 10)]];
AGSPolyline *lineCD = [AGSPolyline polylineWithPoints:@[AGSPointMakeWGS84(0, 10), AGSPointMakeWGS84(10, 0), AGSPointMakeWGS84(5, 10), AGSPointMakeWGS84(0, 0), AGSPointMakeWGS84(10, 10)]];
AGSPolyline *lineE = (AGSPolyline*)[AGSGeometryEngine intersectionOfGeometry1:lineAB geometry2:lineCD];
NSLog(@"lineE: %@", lineE);
}