Perpendicular means that the slope of one line is the opposite reciprocal of the other; bisector means that the line that is perpendicular is cutting the other one exactly in half. So we have to find 2 things about BC: the first is the midpoint which will then serve as the x and y coordinates in our new equation, and second is the slope of it. First things first: the midpoint formula is this: 
. Using our coordinates we fill in that formula like this: 
which of course gives us a midpoint of (7, 6). Now for the slope of the line BC: 
. But since we need the perpendicular slope of that we will take its opposite reciprocal which is 1/2. Now use the x and y coordinates of the midpoint and that newly found slope and write your equation to solve for b. 
. Solving that for b gives you that b = 5/2. So the equation of the line that is the perpendicular bisector of BC (drum roll, please...) is 