1. **State the problem:** Find the coordinates of point P on the line segment connecting the black checker at (2,5) and the white checker at (7,8) such that the ratio of the distance from the black checker to P and from P to the white checker is 2 to 1. 2. **Formula used:** To find a point dividing a segment in the ratio $m:n$, use the section formula: $$P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)$$ where $x_1,y_1$ and $x_2,y_2$ are coordinates of the two points. 3. **Identify values:** Here, $m=2$, $n=1$, $x_1=2$, $y_1=5$ (black checker), $x_2=7$, $y_2=8$ (white checker). 4. **Calculate x-coordinate of P:** $$x_P = \frac{2 \times 7 + 1 \times 2}{2+1} = \frac{14 + 2}{3} = \frac{16}{3}$$ 5. **Calculate y-coordinate of P:** $$y_P = \frac{2 \times 8 + 1 \times 5}{2+1} = \frac{16 + 5}{3} = \frac{21}{3} = 7$$ 6. **Final coordinates:** $$P = \left( \frac{16}{3}, 7 \right) \approx (5.33, 7)$$ Thus, point P is at $\left( \frac{16}{3}, 7 \right)$ on the line segment between the black and white checkers dividing the segment in the ratio 2:1.