A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are respectively:

1. (0, 10) and (-4, 0)

2. (0, -5) and (2, 0)

3. (0, 4) and (-10, 0)

4. (0, -10) and (4, 0)

Let P(0, a) be the point on y-axis and Q(b, 0) be the point on x-axis.

Given, (2, -5) is the mid-point of PQ.

By mid-point formula,

(x, y) = $\Big(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

$\Rightarrow (2, -5) = \Big(\dfrac{0 + b}{2}, \dfrac{a + 0}{2}\Big) \\[1em] \Rightarrow (2, -5) = \Big(\dfrac{b}{2}, \dfrac{a}{2}\Big) \\[1em] \Rightarrow 2 = \dfrac{b}{2} \text{ and } -5 = \dfrac{a}{2} \\[1em] \Rightarrow b = 4 \text{ and } a = -10.$

P(0, -10) and Q(4, 0)

Hence, Option 4 is the correct option.