Answer:
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
