The equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is

Solution:
Given that we have to write equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)
Let us first find the slope of given line AB
The slope "m" of the line is given as:

Here the given points are A(-2,2) and B(5,4)


Thus the slope of line with given points is

We know that product of slopes of given line and slope of line perpendicular to given line is always -1

The perpendicular bisector will run through the midpoint of the given points
So let us find the midpoint of A(-2,2) and B(5,4)
The midpoint formula for given two points is given as:


Substituting the given points A(-2,2) and B(5,4)

Now let us find the equation of perpendicular bisector in point slope form
The perpendicular bisector passes through points (3/2, 3) and slope -7/2
The point slope form is given as:



Thus the equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is found out