The equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is
<h3><u>Solution:</u></h3>
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
<em><u>The slope "m" of the line is given as:</u></em>
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)
<em><u>The midpoint formula for given two points is given as:</u></em>
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
<em><u>The point slope form is given as:</u></em>
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