Question

Find the equation of the perpendicular bisector of AB if the coordinates of A and B are (2,6) and ( 4,6).

Answer 1

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