The formula for determining the midpoint between two lines is expressed as
Midpoint = [(x1 + x2)/2 , (y1 + y2)/2]
From the points given,
x1 = - 1, y1 = - 1
x2 = - 11, y2 = 0
Midpoint = [(- 1 - 11)/2 , (- 1 + 0)/2]
Midpoint = [(- 12/2, - 1/2)]
Midpoint = (- 6, - 1/2)
The next step is to find the slope of the line. The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
Slope = (0 - - 1)/(- 11 - -1)
Slope = 1/- 10
Slope = - 1/10
The perpendicular bisector would have a slope that is a negative reciprocal of the given slope. Thus,
slope = 10
We would write the equation of the line in the slope intercept form which is expressed as
y = mx + c
where m represents slope
Since the line passes through (- 6, - 1/2), we would find the y intercept by substituting x = - 6, y = - 1/2 and m = 10 into the slope intercept equation. It becomes
- 1/2 = - 6 * 10 + c
- 1/2 = - 60 + c
c = - 0.5 + 60 = 59.5
Thus, the equation of the line is
y = 10x + 59.5
The general form is
10x - y = - 59.5