Question

Please help asap!!! i dont understand it

Answer 1

a

Explanation:

A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.

Calculate slope m using the slope formula

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

with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)

m =
`(13-1)/(9-(-7))` =
`(12)/(9+7)` =
`(12)/(16)` =
`(3)/(4)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((3)/(4) )` = -
`(4)/(3)` ← slope of perpendicular bisector

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

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

using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then

midpoint = (
`(-7+9)/(2)`,
`(1+13)/(2)` ) = (
`(2)/(2)`,
`(14)/(2)` ) = (1, 7 )

The equation of a line in slope- intercept form is

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

Here m = -
`(4)/(3)` , then

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

To find c substitute the midpoint (1, 7) into the partial equation

7 = -
`(4)/(3)` + c ⇒ c =
`(21)/(3)` +
`(4)/(3)` =
`(25)/(3)`

y = -
`(4)/(3)` x +
`(25)/(3)` ← equation of perpendicular bisector