Points A and B have co-ordinates (4, y) and (x, 8). The mid-point of AB = (0, 0); the values of x and y are :

1. x = -4, y = 8

2. x = 4, y = -8

3. x = -4, y = -8

4. x = 4, y = 8

By mid-point formula,

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

Substituting values we get :

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

Hence, Option 3 is the correct option.