SOLUTION: Determine whether the parallelogram is a rhombus, rectangle, square or none. Explain. P(7,-1), Q(3,6), R(-1,-1), S(3,-8)?

Question 1121950: Determine whether the parallelogram is a rhombus, rectangle, square or none. Explain. P(7,-1), Q(3,6), R(-1,-1), S(3,-8)?
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.

I will make a blind analysis without making a sketch.

Diagonal PR is horizontal y = -1.


Diagonal QS is vertical   x =  3.


The intersection point of the diagonals is  (3,-1)  and it is the midpoint of diagonal PR; it is also the midpoint of diagonal QS.


Hence,  PQRS  is a rhombus.


Diagonal lengths are  8 (PR)  and  14 (QS).  Hence, PQRS is not a rectangle.


Answer.  PQRS is a rhombus; it is NEITHER a rectangle NOR a square.

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