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 ->  Equations -> 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.      Log On


   

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(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The quadrilateral+PQRS has vertices
P(2,4)
Q(5,1)
R(-1,-2)
S(-4,1)

the opposite sides are:
PQ and RS
PS and QR
use given data to find distance between points or the length of the sides:
P(2,4)
Q(5,1)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%285-%282%29%29%5E2%29%2B%28%281-%284%29%29%5E2%29%29
sqrt%283%5E2%2B-3%5E2%29 The distance is 4.24264068711928.



PQ=4.24264068711928

R(-1,-2)
S(-4,1)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%28-4-%28-1%29%29%5E2%29%2B%28%281-%28-2%29%29%5E2%29%29
sqrt%28-3%5E2%2B3%5E2%29 The distance is 4.24264068711928.


RS=4.24264068711928
so, PQ=RS
if so, then PS and QR must be equal too
let's check it
P(2,4)
S(-4,1)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%28-4-%282%29%29%5E2%29%2B%28%281-%284%29%29%5E2%29%29
sqrt%28-6%5E2%2B-3%5E2%29 The distance is 6.70820393249937.



PS=6.70820393249937
Q(5,1)
R(-1,-2)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%28-1-%285%29%29%5E2%29%2B%28%28-2-%281%29%29%5E2%29%29
sqrt%28-6%5E2%2B-3%5E2%29 The distance is 6.70820393249937.



QR=6.70820393249937
and, PS+=+QR
it is proven that PQRS+is a parallelogram