Point a is located at (4, 1) point b is located at (9, 13)
what are the coordinates of the point that partitions the directed line segment ab in a 4: 1 ratio

Since the line segment is partitioned into a 4:1 ratio, the line segment is divided into 5 equal lengths.

Get the horizontal distance:
9 - 4 = 5
Divide by 5
5/5
Multiply by 4
5/5 x 4 = 4
Add this to the x coordinate of A
4 + 4 = 8

Get the vertical distance:
13 - 1 = 12
Divide by 5
12/5
Multiply by 4
12/5 x 4 = 9.6
Add this to the y coordinate of A
1 + 9.6 = 10.6

The coordinates of the point is
(8, 10.6)