Geometry

Question Analysis:
This question tests the use of the midpoint formula to determine whether the diagonals bisect each other in a coordinate quadrilateral.
The main focus is establishing diagonal bisection → parallelogram.

Key Concept Explanation:
If both diagonals have the same midpoint, then they bisect each other, and the quadrilateral is a parallelogram.

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

Option Analysis:
A: ✅ Correct – midpoints are equal
B: Incorrect – th...