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Given Quadrilateral ABCD has coordinates A (3, -5), B (5, -2), C (10, -4), D (8, -7) Quadrilateral ABCD what polygon?

Answer 1

Aaliyah Anderson

It’s a parallelogram

Given : #A (3,-5), B (5, -2), C (10,-4), D(8,-7)#

Slope #m_(AB) = (-2+5)/(5-3) = 3/2#

Slope #m_(BC) = (-4+2)/(10-5) = -2/5#

Slope #m_(CD) = (-7+4)/(8-10) = 3/2#

Slope #m_(DA) = (-7+5)/(8-3) = -2/5#

Slopes of opposite sides are equal. Hence, they are parallel.

#vec(AB) = srt((5-3)^2 + (-2 + 5)^2) = sqrt13#

#vec(BC) = srt((5-10)^2 + (-2 + 4)^2) = sqrt29#

#vec(CD) = srt((8-10)^2 + (-7 + 4)^2) = sqrt13#

#vec(DA) = srt((8-3)^2 + (-7 + 5)^2) = sqrt29#

Since only opposite sides are parallel and equal, and the product of the slopes of the adjacent sides not equal to (-1), it a simple parallel.

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Answer 2

Avery Allen

Quadrilateral ABCD is a parallelogram.

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