Geometry

Question Analysis:
This is a coordinate geometry question where you are to find a missing vertex in a parallelogram.
The main focus is using the fact that diagonals of a parallelogram bisect each other.

Key Concept Explanation:
In a parallelogram, the diagonals intersect at their midpoints.
So, midpoint of AC = midpoint of BD.

Step-by-Step Solution:
Find midpoint of diagonal AC:
A = (2, −1), C = (11, 10)
→ Midpoint = (2 + 11)/2, (−1 + 10)/2 = (6.5, 4.5)
Let D = (x, y); B = (8, 4)
Midpoint of BD = (8+x)/2,(4+y)/2
Set this equal to (6.5, 4.5):
(8 + x)/2 = 6.5 → 8 + x = 13 → x = 5
(4 + y)/2 = 4.5 → 4 + y = 9 → y = 5
So D = (5, 5)
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