Find the coordinates of the point that divides the line segment joining the points P(5, -2) and Q(9, 6) internally in the ratio of 3 : 1.

Let R be the point whose co-ordinates are (x, y) which divides PQ in the ratio of 3 : 1.

By section formula, x-coordinate is given by,

$x = \dfrac{m$1x2 + m2x1}{m1 + m2} \\[1em] = \dfrac{3 \times 9 + 1 \times 5}{3 + 1} \\[1em] = \dfrac{27 + 5}{4} \\[1em] = \dfrac{32}{4} \\[1em] = 8.

Similarly y-coordinate is given by,

$y = \dfrac{m$1y2 + m2y1}{m1 + m2} \\[1em] = \dfrac{3 \times 6 + 1 \times (-2)}{3 + 1} \\[1em] = \dfrac{18 + (-2)}{4} \\[1em] = \dfrac{16}{4} \\[1em] = 4.

∴ R = (8, 4).

Hence, coordinates of point that divides PQ in the ratio 3 : 1 is (8, 4).