Geometry

Question Analysis:
Classify the quadrilateral using slopes and sides.

Key Concept Explanation:
Parallelogram: Both pairs of opposite sides must be parallel.

Step-by-Step Solution:
AB slope = (1−1)/(3−(−2)) = 0
DC slope = (4−4)/(0−5) = 0 → AB || DC ✅
BC slope = (4−1)/(5−3) = 3/2
AD slope = (4−1)/(0−(−2)) = 3/2 → BC || AD ✅
Two pairs of opposite sides are parallel → parallelogram.
For a quadrilateral to be a rectangle, adjacent sides must be perpendicular (slopes multiply to -1).
Check slopes of adjacent sides:
AB slope = (1−1)/(3−(−2)) = 0
BC slope = (4−1)/(5−3) = 3/2
Product: 0(3/2) = 0  → Not perpendicular.
For a quadrilateral to be a rhombus, all sides must be equal in length.
Points:  and 
Points:  and