Question

Quadrilateral PQRS has vertices P(-1,-1), Q(1,0), R(2,2) S(0,1). What is the most specific name for ABCD?

a. Rhombus
b. Rectangle
c. Parallelogram
d. Square
e. Trapezoid

Answer 1

The most specific name for quadrilateral PQRS is parallelogram.

Step-by-step explanation:

The given quadrilateral PQRS has vertices P(-1,-1), Q(1,0), R(2,2), and S(0,1). To determine the most specific name for this quadrilateral, we need to analyze its properties.

1. First, we calculate the slopes of the sides PQ, QR, RS, and SP. If the slopes are equal, it is a parallelogram. If the slopes of opposite sides are equal, it is a rectangle or a square. If the slopes of both pairs of opposite sides are equal and the lengths of the sides are equal, it is a square.

2. Next, we calculate the lengths of the sides PQ, QR, RS, and SP. If the lengths of opposite sides are equal, it is a parallelogram. If the lengths of both pairs of opposite sides are equal, it is a rhombus. If the lengths of opposite sides are equal and the angles are all right angles (90 degrees), it is a rectangle. If the lengths of both pairs of opposite sides are equal and the angles are all right angles, it is a square.

Based on the calculations, the most specific name for quadrilateral PQRS is parallelogram.