$\begin{array}{1 1}(a)\;2y+3x=20\\(b)\;3y+2x=20\\(c)\;y+3x=10\\(d)\;2y+x=20\end{array}$

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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.

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