Quadrilateral PQRS has vertices P (-3, 2), Q (-1, 4), and R (5, 0). For each of the given coordinates of vertex S, determine whether the quadrilateral is a parallelogram, a trapezoid that is not a parallelogram, or neither. Select the correct answer for each lettered part.

a. S (0, 0)

b. S (3, - 2)

c. S (2, - 1)

d. S (6, - 4)

e. S (5, - 3

it is trapezium in case of a) S (0, 0) it is parallelogram in case of b) S (3, - 2)

And vertex of part c), d) and e) are neither trapezium nor parallelogram.

Step-by-step explanation:

The given Quadrilateral PQRS has vertices P (-3, 2), Q (-1, 4), and R (5, 0).

If we take fourth vertex S as (0, 0) (as shown in figure-1)

we can see that distance between PQ and ST are same 2√2.

so, line PS and RQ are parallel.

Therefore it is trapezium in case of a) S (0, 0)

If we take fourth vertex S as (3, - 2) (as shown in figure-2)

we can see that distance between PQ and SR are same 2√2

and distance between PS and RQ are same √52

Therefore it is parallelogram in case of b) S (3, - 2)

And vertex of part c), d) and e) are neither trapezium nor parallelogram.

The second (b) is the correct one.

a is trapezoid.

c, d, e i think neither.