Question

Please someone help me please i need help with this question answer asap

Answer 1

y = -
`(1)/(3)` x +
`(8)/(3)`

Explanation:

the perpendicular bisector of AB passes through the midpoint of AB at right angles.

find the midpoint using the midpoint formula

with A (- 2, 0 ) and B (0, 6 )

midpoint = (
`(-2+0)/(2)` ,
`(0+6)/(2)` ) = (
`(-2)/(2)` ,
`(6)/(2)` ) = (- 1, 3 )

find the gradient m of AB using the gradient formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = A (- 2, 0 ) and (x₂, y₂ ) = B (0, 6 )

m =
`(6-0)/(0-(-2))` =
`(6)/(0+2)` =
`(6)/(2)` = 3

given a line with gradient m then the gradient of a line perpendicular to it is

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

the equation of a line in gradient- slope form is

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

here m = -
`(1)/(3)` , then

y = -
`(1)/(3)` x + c ← is the partial equation

to find c substitute (- 1, 3 ) into the partial equation

3 =
`(1)/(3)` + c ⇒ c = 3 -
`(1)/(3)` =
`(8)/(3)`

y = -
`(1)/(3)` x +
`(8)/(3)` ← equation of perpendicular bisector