Answer
See below
Work Step by Step
Find the midpoint of the line segment
$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{3+7}{2},\frac{8+14}{2})=(5,11)$
Calculate the slope of AB:
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{14-8}{7-3}=\frac{3}{2}$
Find the slope of the perpendicular bisector:
$-\frac{1}{m}=-\frac{2}{3}$
Use point-slope form:
$y-11=-\frac{2}{3}(x-5)$
