Question

parallelogram ABCD has the following vertices A(0,8) B(8,4) C(2,-8) D(-6,-4) is parallelogram ABCD a rectangle, and why

Answer 1

Answer:

Yes, because BC is perpendicular to AB, and ABCD is a parallelgram.

Answer 2

Yes the parallelogram is a rectangle.

What is distance formula?

The distance between coordinate P(x1 , y1) and coordinate Q(x2 , y2) is calculated using the distance formula: d = √[(x2 - x1)² + (y2 - y1)²]

Given:

ABCD is parallelogram, so its opposite sides are equal in length.

i.e., AB= CD and AD= BC

Now,

d=√(8−0)²+(4−8)

d=√(8)²+(−4)²

d=√64+16

d=√80

d=√(−6−2)²+(−4−(−8))²

d=√(−8)²+(4)²

d=√64+16

d=√80

so, AB = CD

Similarly, AD= BC = √180

Hence, a quadrilateral whose opposite side are equal called as rectangle.

Learn more about this concept here:

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