Question

Which equation represents the perpendicular

bisector of AB whose endpoints are A(8.2) and
B(0,6)?
1: y = 2x - 4

2: y=-1/2x+2

3: y=-1/2x+6

4: y = 2x - 12

Answer 1

1: y = 2x -4

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)

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Point

The midpoint of the given segment is ...

(A+B)/2 = (8 +0, 2 +6)/2 = (4, 4)

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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