Geometry

Question Analysis:
This question asks to classify the polygon using slope and distance properties.
The main focus is checking if both pairs of opposite sides are parallel.

Key Concept Explanation:
Parallelogram: both pairs of opposite sides must be parallel.
Slope formula: (y₂ - y₁)/(x₂ - x₁).
Distance formula: √[(x₂ − x₁)² + (y₂ − y₁)²].
Perpendicular: slopes are negative reciprocals.

Step-by-Step Solution:
AB slope = (1 − 1)/(2 − (−3)) = 0 (horizontal)
DC slope = (5 − 5)/(−2 − 3) = 0 (horizontal) → AB || DC ✅
BC slope = (5 − 1)/(3 − 2) = 4
AD slope = (5 − 1)/(−2 − (−3)) = 4 → BC || AD ✅
Thus, ABCD is a parallelogram.
Distance:
AB = √[(2 − (-3))² + (1 − 1)²] = 5.
DC =...