What is the equation of the perpendicular bisector drawn between the points joining (4,2) and (4, 6) ?

To find the equation of the perpendicular bisector for
line segment joining A(4,2) and
B(4,6).

Solution:

The
perpendicular bisector passes through the midpoint of the line segment joining  A and B
. and is perpendicular to AB.

The mid point of the line AB
is (Mx , My) = ( (Ax+Bx)/2 ,  (Ay+By)/2) ) = ( (4+4)/2 , (2+6)/2 ) =
(4,4).

The slope of the line through the mid point M(4,4)
shoulf be perpendicular to AB.

The slope of AB =
(By-Ay)/(Bx-Ax) = (6-2)/(4-4) = infinite  or AB is parallel to y
axis.

So the perpendicular to AB should be parallel to x
axis ( or perpendicular to y axis). Ao the equation of this line is y =
k.

Since y=k should pass thruogh  mid point of AB , that is
M(4,4).

So y = 4 is the line which is the perpendicular
bisector of A(4,2) and B(4,6)