Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.
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Question

rosalina134 · Answer

@angel @angle @vocaloid

sillybilly123 · Answer

you are going to have to prove, IMHO, that every internal angle is $90^o$.

which is what makes a parallelogram a rectangle

In maths, you can't just say that it looks like a rectangle.  Sadly.

You could spin the co-ordinate system, but that spinning itself would IMHO need some kind of legitimicy.

sorry, i can't help, great question

sillybilly123 · Answer

am i over - complicating, Voca?

Vocaloid · Answer

nah silly you were great ^^ I just wanted to be a bit more specific with the explanation

to help prove the shape is a rectangle, you can show that AB = DC and AD = BC (one of the requirements of a rectangle is having two pairs of opposite sides) as well as showing that each angle is 90 degrees by demonstrating that every pair of adjacent sides makes a 90 degree angle (adjacent sides have opposite reciprocal slopes)

calculating side lengths will require the distance formula/Pythagorean theorem while calculating slopes requires the slope formula

I don't know if they want you to show the actual math, but this is basically the proof in words

sillybilly123 · Answer

geometry is gruelling.

rosalina134 · Answer

Yeah unfortunately they want me to use actual math...Thank you guys though. Geometry is  grueling indeed..

sillybilly123 · Answer

😤

sillybilly123 · Answer

if youy are actually using Euclid's Elements, you deserve sympathy.  i suspect you have been given a bunch of rules that you can use.  just saying

sillybilly123 · Answer

Mmmm, so show what you think proves what you are expected to prove !!??