Geometry

Question Analysis:
This is a reverse application question: the quadrilateral is already known to be a parallelogram, and the missing point is to be determined by using the midpoint property of diagonals.
The main focus is solving for an unknown coordinate using midpoint equality.

Key Concept Explanation:
In a parallelogram, diagonals bisect each other. So, the midpoints of AC and BD must be the same.

Step-by-Step Solution:
AC: A(1, 2), C(9, 10) → Midpoint = ((1+9)/2, (2+10)/2) = (5, 6)
BD: B(7, 4), D(x, y) → Midpoint = ((7+x)/2, (4+y)/2)
Now, set midpoints equal:
(7 + x)/2 = 5 ⇒ 7 + x = 10 ⇒ x = 3