Find an equation for the perpendicular bisector of the line segment whose endpoints (5,-4) and (-9, -8).
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The equation for the perpendicular bisector of the line segment will be:

Step-by-step 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

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:

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6