Explanation

(c)
Let the points be $A(3,\ - 4)$ and $B(5,\ 2)$ and mid point of $AB = (4,\ - 1)$
It is given that the bisecting line intersect the coordinate axes in the ratio $2:1$
$\therefore$ Point of coordinate axes are $(2k,\ 0)$ and $(0,\ k)$. The equation of line passing through the above point is
$y - 0 = \frac{k - 0}{0 - 2k}(x - 2k)$
$\Rightarrow \ y = - \frac{1}{2}(x - 2k)$ …(i)
Since, it passing through the mid point of $AB\ ie,\ (4,\ - 1)$
$\therefore\ - 1 = - \frac{1}{2}(4 - 2k)\ \Rightarrow \ k = 1$
On putting the value of $k$ in Eq. (i), we get
$y = - \frac{1}{2}(x - 2)\ \Rightarrow \ x + 2y = 2$