Question

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.

Answer 1

Answer:

Perpendicular

Step-by-step explanation:

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

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

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)

$m_{AB}$ = $\frac{f-0}{e-0}$ = $\frac{f}{e}$

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

$m_{CD}$ = $\frac{0-e}{f-0}$ = - $\frac{e}{f}$

Thus AB and CD are perpendicular since $\frac{f}{e}$ × - $\frac{e}{f}$ = - 1