Answer:
The equation for the perpendicular bisector of the line segment will be:

Explanation:
Given the endpoints of the line segments
Determining the slope between (5,-4) and (-9, -8)




We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 2/7
Thus, the slope of the the new perpendicular line = – 1/m = (-1)/(2/7)= -7/2
Next, determining the mid-point between (5,-4) and (-9, -8)



Refine

We know that the point-slope form of equation of line is

where
- m is the slope of the line
substituting the slope of the perpendicular line -7/2 and the point (-2, -6)



Subtract 6 from both sides


Therefore, the equation for the perpendicular bisector of the line segment will be:
