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

Question

asked Aug 1, 2017 126k views

2 Answers

Qqq · Answer 1 · 2017-08-02T13:20:26+0000

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.

Volcanic · Answer 2 · 2017-08-06T22:47:52+0000

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

step 1

find the slope of the line segment AB

m=((y2-y1))/((x2-x1))

mAB=((f-0))/((e-0))

mAB=((f))/((e))

step 2

find the slope of the line segment CD

m=((y2-y1))/((x2-x1))

mCD=((0-e))/((f-0))

mCD=((-e))/((f))

$mAB*mCD=((f)/(e) )*((-e)/(f) )\\ =-1$

therefore

the answer is

Line segments AB and CD are perpendicular