Question

Find the equation of the line that is the perpendicular bisector of AB

A y=2/3x+2
B y=-2/3x+2.5
C y=-2/3x+2
D y= -2/3x+13/6

Answer 1

D

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m of AB

m =
`(rise)/(run)` =
`(3)/(2)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((3)/(2) )` = -
`(2)/(3)`

To find the midpoint of AB use the midpoint formula

M = [
`(1)/(2)`(x₁ + x₂ ),
`(1)/(2)` (y₁ + y₂ ) ]

with (x₁, y₁ ) = )0, 0) and (x₂, y₂ ) = (2, 3), thus

M = [
`(1)/(2)`(0 + 2),
`(1)/(2)`(0 + 3 )] = (1,
`(3)/(2)` )

Partial equation of perpendicular bisector is

y = -
`(2)/(3)` x + c

To find c substitute (1,
`(3)/(2)` ) into the partial equation

`(3)/(2)` = -
`(2)/(3)` + c ⇒ c =
`(3)/(2)` +
`(2)/(3)` =
`(13)/(6)`

y = -
`(2)/(3)` x +
`(13)/(6)` → D