Straitforward trigonometric solution could be something like that:

// I've used Tupple<Double, Double> to represent a point;
// You, probably have your own type for it
public static IList<Tuple<Double, Double>> SplitLine(
  Tuple<Double, Double> a, 
  Tuple<Double, Double> b, 
  int count) {

  count = count + 1;

  Double d = Math.Sqrt((a.Item1 - b.Item1) * (a.Item1 - b.Item1) + (a.Item2 - b.Item2) * (a.Item2 - b.Item2)) / count;
  Double fi = Math.Atan2(b.Item2 - a.Item2, b.Item1 - a.Item1);

  List<Tuple<Double, Double>> points = new List<Tuple<Double, Double>>(count + 1);

  for (int i = 0; i <= count; ++i)
    points.Add(new Tuple<Double, Double>(a.Item1 + i * d * Math.Cos(fi), a.Item2 + i * d * Math.Sin(fi)));

  return points;
}

...

IList<Tuple<Double, Double>> points = SplitLine(
  new Tuple<Double, Double>(35.163, 128.001),
  new Tuple<Double, Double>(36.573, 128.707),
  8);

Outcome (points):

(35,163, 128,001)                    // <- Initial point A
(35,3196666666667, 128,079444444444)
(35,4763333333333, 128,157888888889)
(35,633, 128,236333333333)
(35,7896666666667, 128,314777777778)
(35,9463333333333, 128,393222222222)
(36,103, 128,471666666667)
(36,2596666666667, 128,550111111111)
(36,4163333333333, 128,628555555556)
(36,573, 128,707)                    // <- Final point B