We are given the following endpoints
A (2, 4) and B (17, 14)
We need to find point P such that the segment is in the rato of 2:3
Total segments = 2+3 = 5
The x-coordinate of the point P is given by
[tex]\begin{gathered} x_p=x_1+\frac{2}{5}(x_2-x_1) \\ x_p=2_{}+\frac{2}{5}(17-2) \\ x_p=2_{}+\frac{2}{5}(15) \\ x_p=2_{}+6 \\ x_p=8 \end{gathered}[/tex]The y-coordinate of the point P is given by
[tex]\begin{gathered} y_p=y_1+\frac{2}{5}(y_2-y_1) \\ y_p=4+\frac{2}{5}(14-4) \\ y_p=4+\frac{2}{5}(10) \\ y_p=4+4 \\ y_p=8 \end{gathered}[/tex]Therefore, the point P is (8, 8)