Answer: Thus, the answer is (14.5, 14.83).
Step-by-step explanation: Given that A(2, 4) and B(17, 17) are the end points of a directed line segment AB . We are find the point P on the line segment AB which divides it in the ratio AP : PB = 5 : 1. See the attached figure.
The co-ordinates of point P will be
[tex]P\\\\\\=\left(\dfrac{5\times 17+1\times 2}{5+1},\dfrac{5 \times 17+1\times 4}{5+1}\right)\\\\\\=\left(\dfrac{87}{6},\dfrac{89}{6}\right)\\\\\\=(14.5,14.83).[/tex]
Therefore, the co-ordinates of point P are (14.5, 4.83).
Thus, the answer is (14.5, 14.83).
