Question

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

Answer 1

the second (b) is the correct one.
a is trapezoid.
c,d,e i think neither.

Answer 2

• 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.

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.