∆ABC has vertices: (0,0) , (12,6) , (18,0). Find the equations of the lines that contain the three perpendicular bisectors of the triangle.

Question

∆ABC has vertices: (0,0) , (12,6) , (18,0). Find the equations of the lines that contain the three perpendicular bisectors of the triangle.

Answer 1

Slope of AB = (6-0) / (12-0) = 1/2. So, perpendicular bisector of AB has slope -1 / (1/2) = -2 and goes through the midpoint of AB, which is the point ((6, 3). So, an equation of the perpendicular bisector of AB is:

y - 3 = -2(x - 6), or equivalently, y = -2x + 15.

The other two perpendicular bisectors can be found in a similar manner.