Question

A is the point (-1,1), B(3,3) and C is (6,2). The perpendicular bisector of AB has equation y+2x=4. Find the equation of the perpendicular bisector BC.

Answer 1

Line BC has slope -1/3 so the perpendicular bisector will have slope 3. The bisector will have an equation of the form y = mx+b. We know m = 3 and we also know the bisector will pass midway through the line BC, which is (4 1/2, 2 1/2). Plug this coordinate into y = 3x + b.
So b = -11 and the full equation is
y = 3x - 11