Point A lies on x-axis and point B lies on y-axis. If P(2, -2) bisects the line segment AB, the co-ordinates of A are :

1. (4, 0)

2. (0, 4)

3. (-4, 0)

4. (0, -4)

Given,

Point A lies on x-axis.

∴ Let point A be (x, 0).

Point B lies on y-axis.

∴ Let point B be (0, y).

P(2, -2) bisects the line segment AB or P is the mid-point of AB.

By mid-point formula,

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

Substituting values we get :

$\Rightarrow (2, -2) = \Big(\dfrac{x + 0}{2}, \dfrac{0 + y}{2}\Big) \\[1em] \Rightarrow (2, -2) = \Big(\dfrac{x}{2}, \dfrac{y}{2}\Big) \\[1em] \Rightarrow \dfrac{x}{2} = 2 \text{ and } \dfrac{y}{2} = -2 \\[1em] \Rightarrow x = 4 \text{ and } y = -4.$

Co-ordinates of A = (x, 0) = (4, 0).

Hence, Option 1 is the correct option.