GEOMETRY: Find an equation for the perpendicular bisector of the line segment whose endpoints are (9,-8) and (−1,−4).

The equation is;

2y = 5x-32

Step-by-step explanation:

Firstly, we find the mid-point segment

we can use the midpoint segment formula for this

Mathematically, we have this as:

(x,y) = (x1 + x2)/2, (y1 + y2)/2

(x,y) = (9-1)/2, (-8-4)/2

= (4,-6)

Let us find the slope of the given line segment

Mathematically, that will be;

m = (y2-y1)/(x2-x1) = (-4 + 8)/(-1-9) = 4/-10 = -2/5

Now, if two lines are perpendicular, the products of their slopes is equal to -1

so;

m1 * m2 = -1

-2/5 * m2 = -1

m2 = (-1 * 5)/-2

m2 = -5/-2 = 5/2

Since the perpendicular bisector is expected to pass through the midpoint,

we have the equation as slope 5/2 and point (4,-6)

so we use the point-slope equation form

That will be;

y-y1 = m(x-x1)

y+ 6 = 5/2(x-4)

2y + 12 = 5x - 20

2y = 5x -20-12

2y = 5x - 32