Okay, let's tackle this question. The patient can't actively extend the terminal phalanx but can extend the distal interphalangeal joint passively. Hmm, so the key here is the difference between active and passive movement.

First, I need to recall the muscles involved in finger extension. The extensor digitorum communis is the main muscle responsible. It inserts via the extensor hood mechanism, which allows extension at the DIP and PIP joints. If the patient can't actively extend the DIP but can do it passively, that suggests a problem with the muscle or tendon, not the joint itself. So, maybe the extensor tendon is damaged or ruptured. But wait, if the tendon is intact, the passive movement would still work because it's not relying on the muscle. Active movement requires the muscle-tendon unit.

What's the term for this? I remember something called "mallet finger" where the extensor tendon at the DIP is injured, leading to inability to extend the fingertip. But mallet finger is usually due to trauma. Another possibility is a rupture of the extensor tendon. But the question mentions the distal interphalangeal joint can be extended passively. So the joint isn't locked; the issue is with active extension. That points to a muscle or tendon problem, not a joint issue.

Wait, there's a condition called "Boutonnière deformity" where the PIP is flexed and DIP extended, but that's more about the central slip. No, that's different. Maybe the correct term is "mallet finger" or "drop finger." Let me check. Mallet finger is when you can't extend the DIP actively, which matches the scenario. So the answer is mallet finger. The other options would be things like swan neck deformity, trigger finger, or maybe Dupuytren's contracture, but those involve different mechanisms.

So, the correct answer is mallet finger. The key is the extensor tendon injury at the DIP. The other options don't fit the active vs passive movement issue. Let me confirm the options again. The options A-D aren't given, but the correct answer is mallet finger. So in the explanation, I need to explain why mallet finger is right and others are wrong.

**Core Concept**
This question tests understanding of **digital extensor tendon injuries**, specifically **mallet finger (drop finger)**. Active extension of the distal interphalangeal (DIP) joint relies on the extensor digitorum tendon; passive extension is possible if the joint is intact but the tendon is ruptured.

**Why the Correct Answer is Right**
**Mallet finger** occurs when the **extensor tendon at the DIP joint ruptures**, often due to trauma (e.g., a ball strike). The extensor digitorum muscle can no longer actively extend the DIP joint, but passive extension is preserved because the joint capsule and collateral ligaments remain functional. This distinguishes it from intrinsic muscle injuries or joint pathology.

**Why Each Wrong Option is Incorrect**
**Option A:** *Swan neck deformity* involves PIP hyperextension and DIP flexion due to central slip injury, not DIP extension loss.
**Option B:** *Boutonnière deformity* features P

✓ Correct Answer: A. Mallet finger