Geometry

Question Analysis:
This question involves classifying a quadrilateral using coordinate geometry.
The main focus is determining whether ABCD is a rectangle, by checking for parallel opposite sides and right angles (via slopes).

Key Concept Explanation:
A rectangle must meet two main conditions:
Opposite sides are parallel (equal slopes).
Adjacent sides are perpendicular (slopes are negative reciprocals).
We'll check all four sides using slope and also confirm side lengths for full clarity.

Step-by-Step Solution:
Step 1: Compute slopes of all sides
Slope of AB = (0 − 0)/(4 − 0) = 0/4 = 0
Slope of CD = (3 − 3)/(0 − 4) = 0/−4 = 0
→ AB ∥ CD ✔
Slope of BC = (3 − 0)/(4 − 4) = 3/0 → undefined
Slope of DA = (0 − 3)/(0 − 0) = −3/0 → also undefined
→ BC ∥ DA ✔
Now check perpendicularity:
Slope of AB = 0; slope of BC = undefined → perpendicular ✔
Slope of CD = 0; slope of DA = undefined → perpendicular ✔
→ All adjacent sides are perpendicular, forming right angles
Step 2: Check side lengths
AB = √[(4 − 0)² + (0 − 0)²] = √[16 + 0] = 4
BC = √[(4 − 4)² + (3 − 0)²] = √[0 + 9] = 3
CD = √[(0 − 4)² + (3 − 3)²] = √[16 + 0] = 4