Question

Please help i’m confused

Answer 1

y =
`(5)/(2)` x - 1

Explanation:

the perpendicular bisector of PQ passes through the midpoint of PQ at right angles to PQ

We require to find the midpoint and slope of PQ

using the midpoint formula to find the midpoint M of PQ

M = (
`(x_(1)+x_(2) )/(2)` ,
`(y_(1)+y_(2) )/(2)` )

let (x₁, y₁ ) = P (- 5, 1 ) and (x₂, y₂ ) = Q (5, - 3 )

substitute these values into the formula for M

M = (
`(-5+5)/(2)` ,
`(1-3)/(2)` ) = (
`(0)/(2)` ,
`(-2)/(2)` ) = (0, - 1 )

find the slope m of PQ using the slope formula

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

let (x₁, y₁ ) = P (- 5, 1 ) and (x₂, y₂ ) = Q (5, - 3 )

substitute these values into the formula for m

m =
`(-3-1)/(5-(-5))` =
`(-4)/(5+5)` =
`(-4)/(10)` = -
`(2)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(2)/(5) )` =
`(5)/(2)`

the perpendicular bisector has a slope of
`(5)/(2)` and passes through the point (0, - 1 )

the equation of a line in slope- intercept form is

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

using m =
`(5)/(2)` and y- intercept = (0, - 1 ) , so c = - 1

y =
`(5)/(2)` x - 1 ← equation of perpendicular bisector