Point $P\Big(\dfrac{a}{8}, 4\Big)$ is the mid-point of the line segment joining the points A(-5, 2) and B(4, 6). Then, the value of a is:

1. -8

2. -4

3. 2

4. 4

Given,

$P\Big(\dfrac{a}{8}, 4\Big)$ is the mid-point of the line segment joining the points A(-5, 2) and B(4, 6).

By mid-point formula,

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

Substituting values we get :

$\Rightarrow \Big(\dfrac{a}{8}, 4\Big) = \Big(\dfrac{-5 + 4}{2}, \dfrac{2 + 6}{2}\Big) \\[1em] \Rightarrow \Big(\dfrac{a}{8}, 4\Big) = \Big(\dfrac{-1}{2}, 4\Big)$

Comparing the x-coordinates, we get :

$\Rightarrow \dfrac{a}{8} = \dfrac{-1}{2} \\[1em] \Rightarrow a = \dfrac{-8}{2} \\[1em] \Rightarrow a = -4.$

Hence, Option 2 is the correct option.