Quadrilateral PQRS has vertices P(0, 4), Q(6, 4), R(4, 0), and S(−2, 0). What is the most specific classification of quadrilateral PQRS?

📌 Step 1: Check for parallel sides
PQ: slope = (4−4)/(6−0) = 0 (horizontal)
SR: slope = (0−0)/(4−(−2)) = 0 (horizontal)
PQ ∥ SR ✓

PS: slope = (0−4)/(−2−0) = −4/−2 = 2
QR: slope = (0−4)/(4−6) = −4/−2 = 2
PS ∥ QR ✓

📌 Step 2: Two pairs of parallel sides → parallelogram

📌 Step 3: Check if it's a special parallelogram
PQ = 6, SR = 6, PS = √(4+16) = √20, QR = √(4+16) = √20
All sides NOT equal → not a rhombus
Slopes of adjacent sides: 0 and 2 → product ≠ −1 → not perpendicular → not a rectangle

📌 Answer: PQRS is a parallelogram.

💡 Tip: To classify a quadrilateral on a coordinate plane:
1. Check slopes for parallel sides
2. Check distances for equal sides
3. Check slope products for right angles