Respuesta :

taskmasters
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. 
calculista

we have that

[tex] A(0, 0)\\B(e, f)\\ C(0, e)\\D(f, 0) [/tex]


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 [tex] -1 [/tex]


step 1

find the slope of the line segment AB

[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]

[tex] mAB=\frac{(f-0)}{(e-0)} [/tex]

[tex] mAB=\frac{(f)}{(e)} [/tex]


step 2

find the slope of the line segment CD

[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]

[tex] mCD=\frac{(0-e)}{(f-0)} [/tex]

[tex] mCD=\frac{(-e)}{(f)} [/tex]


[tex] mAB*mCD=(\frac{f}{e} )*(\frac{-e}{f} )\\ =-1 [/tex]

therefore


the answer is

Line segments AB and CD are perpendicular

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