Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
To find D and E use the midpoint formula
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( ,
)
Here (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(2, - 2) , then
D = (,
) = (3, 2 ) and
let (x₁, y₁ ) = B(2, - 2 ) and (x₂, y₂ ) = C(- 2, - 4 ), then
E = ( ,
) = (1, 1 )
Use the slope formula to find slopes of DE and BC
m =
with (x₁, y₁ ) = D(3, 2) and (x₂, y₂ ) = E(1, 1), then
=
=
=
Repeat with (x₁, y₁ ) = B(2, - 2) and (x₂, y₂ ) = C(- 2, - 4), then
=
=
=
Since the slopes are equal then DE and BC are parallel lines