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Find anequation for the perpendicular bisector of the line segment whose endpointsare (5,-4) and (-9, -8).

Sagot :

First, we need to find the slope of the line:

Let:

(5, -4) = (x1,y1)

(-9, -8) = (x2,y2)

m = (y2-y1)/(x2-x1) = (-8-(-4))/(-9-5) = -4/-14 = 2/7

Also, we need to find the midpoint:

let:

MP = (xp,yp)

xp= (x1+x2)/2 = (5-9)/2 = -2

yp = (y1+y2)/2 = (-4-8)/2 = -6

MP = (-2, -6)

Now, the slope for the perpendicular bisector is -m = -7/2

y = -mx + b

Using the midpoint

-6 = -7/2(-2) + b

-6 = 7 + b

Solving for b:

b = -13

Therefore, the equation for the perpendicular bisector is:

y = -7x/2 - 13

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