Geometry

Question Analysis:
This question evaluates the application of the diagonal bisection condition using coordinate geometry.
The main focus is on checking whether the midpoints of diagonals are the same.

Key Concept Explanation:
In coordinate geometry, if the midpoints of both diagonals are equal, then the diagonals bisect each other → the quadrilateral is a parallelogram.

Step-by-Step Solution:
Diagonal AC: A(1, 2) and C(7, 0)
Midpoint = ((1 + 7)/2, (2 + 0)/2) = (4, 1)
Diagonal BD: B(5, 4) and D(3, -2)
Midpoint = ((5 + 3)/2, (4 + (-2))/2) = (4, 1)
Midpoints match → diagonals bisect each other → parallelogram.

Option Analysis:
A: ✅ Correct ...