Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints at a(-2,2) and b(5,4)

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

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

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step-by-step explanation: