Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A(1,4) and B(-5, -2).

The equation of the line in point slope form is
:

y-y1 = m(x-x1) which has a slope m amd passes through the point
(x1,y1).

A(1,4) and B (-5, -2) has the mid point M (x,y) given
by:

M(x,y) = ( (Ax +Bx)/2 , (Ay+By)/2 )
=

Mx = (1-5)/2 = -2.

 My = (4-2)/2 =
1.

Therefore  M(x,y) = M(-2 , 1).

Slope
of AB = m = (By - Ay)/(Bx- Ax) =  (-2-4)/(-5-1) = 1.

Therefore the
slope a line perpendicular to AB = -1/m = -1/1 = -1.

Therfore the
equation of the line with slope -1 and passing through the mid point M(-2 , 1) of A and B   in
point slope form is given by:

y -1 =
(-1)(x-(-2)). Or

y-1 = -1
(x+2).