P divides the distance between A(-2, 1) and B(1, 4) in the ratio 2:1. Calculate the coordinates of point P.

Let (x, y) be the coordinates of the point P which divides the line segment joining A(-2, 1) and B(1, 4) in the ratio 2 : 1.

∴ Coordinates of P are $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big).

Putting the values from question in above formula we get,

$\Rightarrow \Big(\dfrac{2 \times 1 + 1 \times (-2)}{2 + 1}, \dfrac{2 \times 4 + 1 \times 1}{2 + 1}\Big) \\[1em] = \Big(\dfrac{2 - 2}{3}, \dfrac{8 + 1}{3}\Big) \\[1em] = (0, 3).$

Hence, the coordinates of P are (0, 3).