Given the points A(0, 0), B(e, f), C(0, e) and D(f, 0), determine if line segments AB and CD are parallel, perpendicular or neither.

Perpendicular

Step-by-step explanation:

Calculate the slopes m of the segments using the slope formula.

m =

Parallel lines have equal slopes

The product of the slopes of perpendicular lines equals - 1

(x₁, y₁ ) = A(0, 0) and (x₂, y₂ ) = B(e, f)

= =

Repeat with (x₁, y₁ ) = C(0, e) and (x₂, y₂ ) = D(f, 0)

= = -

Thus AB and CD are perpendicular since × - = - 1