1. **Problem:** Find the coordinates of point D that divides the segment RS externally in the ratio 4:1, where R(2, 3) and S(8, 9). 2. **Formula:** For external division of a segment joining points $R(x_1, y_1)$ and $S(x_2, y_2)$ in ratio $m:n$, the coordinates of point $D$ are given by: $$D = \left( \frac{mx_2 - nx_1}{m-n}, \frac{my_2 - ny_1}{m-n} \right)$$ 3. **Substitute values:** Here, $m=4$, $n=1$, $x_1=2$, $y_1=3$, $x_2=8$, $y_2=9$. $$x_D = \frac{4 \times 8 - 1 \times 2}{4 - 1} = \frac{32 - 2}{3} = \frac{30}{3} = 10$$ $$y_D = \frac{4 \times 9 - 1 \times 3}{4 - 1} = \frac{36 - 3}{3} = \frac{33}{3} = 11$$ 4. **Answer:** The coordinates of point D are $(10, 11)$. This means the depot should be built at point D(10, 11) along the extension of the track beyond station S.