If A ( 4 , 7 ) ,   B ( - 7 , 8 ) and C ( 1 , 2 ) are the vertices of ∆ A B C , then the equation…

The slope of the side $AB$ is $\frac{8-7}{-7-4}=-\frac{1}{11}$
Hence, the slope of the line which is perpendicular to $AB$ is $\frac{1}{-\left(-{\displaystyle \frac{1}{11}}\right)}=11$  (Say $m$)

Now, say, point $D$ is the mid-point of the line $AB$,

Hence, the co ordinate of point $D$ is $\left(\frac{-3}{2}, \frac{15}{2}\right)$.
Now, the equation of perpendicular bisector will be the equation of the line which passes through point $D$ and perpendicular to the line $AB$ is

$y-\frac{15}{2}=m\left(x-\left(-\frac{3}{2}\right)\right)$

$\Rightarrow y-\frac{15}{2}=11\left(x-\left(-\frac{3}{2}\right)\right)$

$\Rightarrow y-\frac{15}{2}=11\left(x+\frac{3}{2}\right)$

$\Rightarrow 11x-y+24=0$