The ratio in which the line segment joining A(2, -3) and B(5, 6) is divided by x-axis is :

1. 1 : 2

2. 2 : 1

3. 3 : 5

4. 2 : 3

Let the point where x-axis intersects the line segment be P(x, 0).

Let the ratio in which P divides AB be m₁ : m₂.

By section-formula (using y–coordinate),

$\Rightarrow y = \Big(\dfrac{m$1y2 + m2y1}{m1 + m2}\Big) \\[1em] \Rightarrow 0 = \dfrac{m1 \times 5 + m2 \times (-3)}{m1 + m2} \\[1em] \Rightarrow 0 = 5m1 - 3m2 \\[1em] \Rightarrow 5m1 = 3m2 \\[1em] \Rightarrow \dfrac{m1}{m2} = \dfrac{3}{5}.

Thus, the required ratio is 3 : 5.

Hence, Option 3 is the correct option.