Coordinate proof of a rectangle

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So I took a state test today and I'm not sure if I messed up or if I will get partial credit for my work, but here goes. We had to prove a quadrilateral was a rectangle and I showed that all the adjacent slopes were negative reciprocal giving it all right angles. IS THAT ENOUGH? Did I have to show it was a parallelogram first?

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That is correct.

The right angle information shows that the alternating side are parallel, which shows that is is a parallelogram.

The right angle info shows that it is a rectangle.