How do you prove that quadrilateral ABCD is a parallelogram with A(-2,-1) B(1,2) C(5,2) D (2,-1) using slope?

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Answer 1 · 2016-11-22T07:24:42

Please see below.

With corners as #A(-2,-1)#, #B(1,2)#, #C(5,2)# and #D(2,-1)#, let us find slopes of each side of the parallelogram #ABCD#.

Slope of #AB# is #(2-(-1))/(1-(-2))=3/3=1#

Slope of #BC# is #(2-2)/(5-1)=0/4=0#

Slope of #CD# is #((-1-2)/(2-5)=(-3)/(-3)=1#

Slope of #DA# is #(-1-(-1))/(2-(-2))=0/4=0#

As slopes of alternate sides of quadrilateral are equal, alternate sides are parallel to each other

and #ABCD# is a parallelogram.