SOLUTION: The quadrilateral PQRS has vertices P(2,4), Q(5,1), R(-1,-2) and S(-4,1). Prove that PQRS is a parallelogram by showing that the opposite sides are equal.

Algebra.Com
Question 1165801: The quadrilateral PQRS has vertices P(2,4), Q(5,1), R(-1,-2) and S(-4,1). Prove that PQRS is a parallelogram by showing that the opposite sides are equal.
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
The quadrilateral has vertices
(,)
(,)
(,)
(,)

the opposite sides are:
and
and
use given data to find distance between points or the length of the sides:
(,)
(,)
Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 4.24264068711928.





(,)
(,)
Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 4.24264068711928.



so,
if so, then and must be equal too
let's check it
(,)
(,)
Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 6.70820393249937.




(,)
(,)
Solved by pluggable solver: Distance Between 2 points
The distance formula is . Plug in the numbers,

The distance is 6.70820393249937.




and,
it is proven that is a parallelogram




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