Mid-point of the points $A(1,2)$ & $B(7,6)$ is $C(x,y)$
$x=\large\frac{1+7}{2}$
$x=4$
$y=\large\frac{2+6}{2}$
$y=4$
Hence straight line passes through (4,4)
BC is perpendicular to straight line.Hence slope of $BC=\large\frac{6-4}{7-4}=\frac{2}{3}$
So the slope of straight line will be $-\large\frac{3}{2}$
Hence equation of straight line is $(y-4)=-\large\frac{3}{2}$$(x-4)$
$2y-8=-3x+12$
$2y+3x=20$
Hence (a) is the correct answer.