Explanation

(c)
The equation of straight line equally inclined to the axes is $\frac{x}{a} + \frac{y}{a} = 1\ \Rightarrow \ x + y = a$. Since, it is equidistant from the points $(1,\ - 2)$ and (3, 4), so perpendicular distances from these points on the line will be equal.
$\Rightarrow \ \left| \frac{1 - 2 - a}{\sqrt{1^{2} + 1^{2}}} \right| = \left| \frac{3 + 4 - a}{\sqrt{1^{2} + 1^{2}}} \right|$
$\Rightarrow \ \frac{1 + a}{\sqrt{2}} = \frac{7 - a}{\sqrt{2}}$
$\Rightarrow \ 2a = 6\ \Rightarrow \ a = 3$
$\therefore$ Equation is $x + y - 3 = 0$
But, given equation is $ax + by + c = 0$
$\therefore a = 1,\ b = 1,\ c = - 3$