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