Given a line segment a(16, 8) and b(1, 3) what are the coordinates or the line segment partitioned two-fifths from a to b.

Partitioning means to find the dividing point between two points.
This is done by prorating the difference in x- and y-coordinates, and adding to the first.

We will take the first point (from A to B) as A(16,8).
The difference is B-A, i.e.
(1,3)-(16,8) = (-15,-5)
2/5 of the difference is (2/5)*(-15,-5) = (-6,-2)
Add the difference to the first coordinates (point A) gives
Point of division = (16,8)+(-6,-2) = (16-6, 8-2) = (10,6)