**Core Concept:** The metacarpophalangeal (MP) joint is a hinge joint in the finger, which allows flexion and extension movements. Injury to a specific nerve can lead to loss of function in these joints.

**Why the Correct Answer is Right:** The correct answer is due to injury to the median nerve, specifically the branch of the median nerve called the superficial palmar arch (SPA). The SPA innervates the intrinsic muscles of the hand, including those responsible for extension of the MP joint. Injury to this nerve can result in weakness or loss of function in these muscles, leading to the inability to extend the MP joint.

**Why Each Wrong Option is Incorrect:**
A. Ulnar nerve: The ulnar nerve is responsible for flexion movements in the hand, not extension.
B. Radial nerve: Similar to the ulnar nerve, the radial nerve is responsible for flexion movements in the hand, not extension.
C. Brachial plexus: This term refers to a group of nerves, not a single nerve responsible for MP joint extension.

**Clinical Pearl:** A thorough clinical examination, including assessing the strength and function of the muscles innervated by the SPA, is crucial in diagnosing nerve injuries and guiding appropriate clinical management.

**Correct Answer: .**