In the given figure, P(4, 2) is mid-point of line segment AB. Find the co-ordinates of A and B.

Since, A lie on x-axis, let its co-ordinates be (x, 0) and B lie on y-axis, let its co-ordinates be (0, y).

P is mid-point of AB.

By formula,

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

Substituting value we get,

$P = \Big(\dfrac{0 + x}{2}, \dfrac{y + 0}{2}\Big) \\[1em] \Rightarrow (4, 2) = \Big(\dfrac{x}{2}, \dfrac{y}{2}\Big) \\[1em] \therefore 4 = \dfrac{x}{2} \text{ and } 2 = \dfrac{y}{2} \\[1em] \Rightarrow x = 8 \text{ and } y = 4.$

A = (x, 0) = (8, 0) and B = (0, y) = (0, 4).

Hence, the co-ordinates of points A and B are (8, 0) and (0, 4).