A point P divides the line segment joining the points A(1, 3) and B(5, 9) in the ratio 1 : 2, the co-ordinates of the point P are :

1. $\Big(\dfrac{7}{3}, 5\Big)$

2. $\Big(7, \dfrac{5}{3}\Big)$

3. $\Big(\dfrac{7}{3}, \dfrac{5}{3}\Big)$

4. $\Big(\dfrac{7}{3}, \dfrac{13}{3}\Big)$

Let point P be (x, y).

Given,

m₁ : m₂ = 1 : 2

By section-formula,

(x, y) = $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Substituting values we get :

$\Rightarrow (x, y) = \Big(\dfrac{1 \times 5 + 2 \times 1}{1 + 2}, \dfrac{1 \times 9 + 2 \times 3}{1 + 2}\Big) \\[1em] = \Big(\dfrac{5 + 2}{3}, \dfrac{9 + 6}{3}\Big) \\[1em] = \Big(\dfrac{7}{3}, \dfrac{15}{3}\Big) \\[1em] = \Big(\dfrac{7}{3}, 5\Big).$

Hence, Option 1 is the correct option.