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Question
Find the equation of the perpendicular bisector of AB if the coordinates of A and B are (2,6) and ( 4,6).
Solution
Let I be the perpendicular bisector of AB
Slope of AB = `(-6 -6)/(4 + 2) = (-12)/6` = -2
Slope of I i.e slope of line perpendicular to AB = `1/2`
Let I intersects AB at P,
`therefore` AP : PB = 1 : 1
Coordinates of P are,
P(x1y1) = P`((-2 + 4)/2, (6 - 6)/2)` = P(1, 0)
Equation of I is `("y" - "y"_1)/("x" - "x"_1)` = slope
`("y" - 0)/("x" - 1) = 1/2`
x - 1 = 2y
x - 2y - 1 = 0
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