Explanation

(a)
Equation of the line passing through $( - 4,\ 6)$ and (8, 8) is
$y - 6 = \left( \frac{8 - 6}{8 + 4} \right)(x + 4)$
$\Rightarrow y - 6 = \frac{2}{12}(x + 4)$
$\Rightarrow 6y - 36 = x + 4\ \Rightarrow 6y - x - 40 = 0$ …(i)
Now, equation of any line perpendicular to the Eq. (i), is
$6x + y + \lambda = 0$ …(ii)
This line passes through the mid point of $( - 4,\ 6)$ and (8, 8) is
$\left( \frac{- 4 + 8}{2},\frac{6 + 8}{2} \right),\ ie,\ (2,\ 7)$
$\therefore 6 \times 2 + 7 + \lambda = 0$
$\Rightarrow 19 + \lambda = 0\ \Rightarrow \lambda = - 19$
On putting $\lambda = - 19$ in Eq. (ii), we get the equation of required line which is
$6x + y - 19 = 0$