The coordinates of the point on x-axis which divides the line segment joining the points (2, 3) and (5, -6) in the ratio 1 : 2 are :

1. (2, 0)

2. (-2, 0)

3. (3, 0)

4. (-3, 0)

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 :

$\Rightarrow (x, y) = \Big(\dfrac{1 \times 5 + 2 \times 2}{1 + 2}, \dfrac{1 \times (-6) + 2 \times 3}{1 + 2}\Big) \\[1em] = \Big(\dfrac{5 + 4}{3}, \dfrac{-6 + 6}{3}\Big) \\[1em] = \Big(\dfrac{9}{3}, \dfrac{0}{3}\Big) \\[1em] = (3, 0).$

Hence, Option 3 is the correct option.