The perpendicular bisector of the line segment joining . . .

Question : The perpendicular bisector of the line segment joining the points A(1,5) and B(4,6) cuts the y-axis at 

a) (0,13)

b) (0,-13)

c) (0,12)

d) (13,0)

Doubt by Gauri & Saumya

Solution : 

AB is the given line segment.

A (1,5)
B (4,6)

PM is the perpendicular bisector of AB

Perpendicular bisector PM will intersect y-axis at (0,y)

PA = PB 

The required coordinate of point P will be (0,13)

Hence, a) would be the correct option.