Equation of a line is  .
.
<h3>What is a perpendicular bisector of the line segment?</h3>
A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.
Given that,
Endpoints of the line segment are ( ) = (4, 1) and (
) = (4, 1) and ( ) = (2, -5).
) = (2, -5).
First find the midpoints of the given line segment.
M = 
     =  
M   =  
Now, Find the slope of the line :
It is perpendicular to the line with (4,1) and (2,-5)
Slope between ( ) and (
) and ( ) =
) = 
so,
 the slope between (4,1) and (2,-5)  =  
                                                          = 3
perpendicular lines have slopes the multiply to get -1
3 times m=-1
m= 
The equation of a line that has a slope of m and passes through the midpoints M(3,-2)  is



if we want slope intercept form


If we want standard form


Hence, Equation of a line is  .
.
To learn more about perpendicular bisector of the line segment from the given link:
brainly.com/question/4428422
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