we have that
A(1,3) and B(1,5)
we know that
the equation of the perpendicular bisector of AB go through the midpoint of AB
so
step 1
find the slope m AB
m=(y2-y1)/(x2-x1)----> m=(5-3)/(1-1)-----> is not defined
because is a vertical line
hence
the perpendicular bisector of AB is a horizontal line
step 2
find the midpoint AB
Mx=(x1+x2)/2-----> Mx=(1+1)/2----> Mx=1
My=(y1+y2)/2-----> My=(5+3)/2----> My=4
the midpoint AB=(1,4)
the equation of the perpendicular bisector of AB is
y=4
the answer is
y=4
see the attached figure
