Triangle abc has vertices a(0 0) b(6 8) and c(8 4). which equation represents the perpendicular bisector of bc

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