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.
parallel
perpendicular
neither

Answer 1

we have that

$A(0, 0)\\B(e, f)\\ C(0, e)\\D(f, 0)$

we know that

If two lines are parallel

then

their slopes are equals

and

if two lines are perpendicular

then

the product of their slopes is equal to $-1$

step 1

find the slope of the line segment AB

$m=\frac{(y2-y1)}{(x2-x1)}$

$mAB=\frac{(f-0)}{(e-0)}$

$mAB=\frac{(f)}{(e)}$

step 2

find the slope of the line segment CD

$m=\frac{(y2-y1)}{(x2-x1)}$

$mCD=\frac{(0-e)}{(f-0)}$

$mCD=\frac{(-e)}{(f)}$

$mAB*mCD=(\frac{f}{e} )*(\frac{-e}{f} )\\ =-1$

therefore

the answer is

Line segments AB and CD are perpendicular

Answer 2

Given the points, when point A, B, C, D are plotted, and connect AB and CD to form a segment, they are not neither parallel nor perpendicular.