Answer:
1: y = 2x -4
Step-by-step explanation:
The perpendicular bisector of the given segment is the line through its midpoint that has a slope that is the opposite reciprocal of the segment's slope.
Slope
The slope of the given segment can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (6 -2)/(0 -8) = 4/-8 = -1/2
The opposite reciprocal of this is ...
m' = -1/(-1/2) = 2 . . . . (eliminates answer choices 2 and 3)
__
Point
The midpoint of the given segment is ...
(A+B)/2 = (8 +0, 2 +6)/2 = (4, 4)
__
Y-intercept
The y-intercept of the perpendicular bisector can be found from ...
b = y -mx
b = 4 -(2)(4) = -4
Then the equation of the perpendicular bisector is ...
y = 2x -4
