Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = 
with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2)
m =
=
= - 2
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Find the midpoint using the midpoint formula
M =(
,
)
=
,
) = (2, - 2 )
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Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= 
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The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m =
, thus
y =
x + c ← is the partial equation
To find c substitute (2, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 2 - 1 = - 3
y =
x - 3 ← equation of perpendicular bisector