Answer:
a
Step-by-step explanation:
A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.
Calculate slope m using the slope formula
m = 
with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)
m =
=
=
= 
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= -
← slope of perpendicular bisector
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
(
,
)
using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then
midpoint = (
,
) = (
,
) = (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 = -
, then
y = -
x + c ← is the partial equation
To find c substitute the midpoint (1, 7) into the partial equation
7 = -
+ c ⇒ c =
+
= 
y = -
x +
← equation of perpendicular bisector