Determine whether the parallelogram is a rhombus, rectangle, square, or none. Explain. Q(1, 3), R(3, 4), S(5, 3), T(3, 2)

Select one:

A. QRST is a rhombus that is not a square because its diagonals are perpendicular but not congruent.

B. QRST is a rectangle that is not a square because its diagonals are congruent but not perpendicular.

C. QRST is a square because its diagonals are both perpendicular and congruent.

D. QRST is none of these because its diagonals are neither congruent nor perpendicular.

Step-by-step explanation:

The diagonals of the given parallelogram are QS and RT. We would first determine if its diagonals are congruent.

QS = √(1 - 5)² + (3 - 3)² = 16

RT = √(3 - 3)² + (4 - 2)² = 4

Since QS ≠ RT, it means that they are not congruent and this means that the parallelogram is not a rectangle.

Let us check if the diagonals are perpendicular.

Slope of QS = (3 - 3)/(5 - 1) = 0/4

Slope of RT = (2 - 4)/(3 - 3) = - 2/0

The slopes are not opposite reciprocals. It means that the diagonals are not perpendicular. Therefore, the correct option is

D. QRST is none of these because its diagonals are neither congruent nor perpendicular.