SOLUTION: If A(2 3) B(p -2) and C(-1 1) and D(3 r) are tthe vertices of a parallelogram ABCD calculated the value of p and of r

Question 1067636: If A(2 3) B(p -2) and C(-1 1) and D(3 r) are tthe vertices of a parallelogram ABCD calculated the value of p and of r
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For ABCD to be a parallelogram,
opposite sides must have equal length and equal slope.
The easiest way to do that is to consider vectors.
We need to have
or .
If one of those pairs of opposite sides complies,
the other pair is forced to do so too.
The only problem would be if we ended with all 4 points being co-linear.
==

So, translates into the system of equations
---> .
The solution for is the same.
So, and ,
and the parallelogram is shown below

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