**Core Concept**
Hemiplegia refers to the paralysis of one side of the body, typically resulting from damage to the brain's motor control systems. The corticospinal tract is a crucial pathway involved in motor control, originating from the cerebral cortex and descending through the brainstem and spinal cord.

**Why the Correct Answer is Right**
The corticospinal tract is primarily responsible for transmitting motor signals from the brain to the muscles. Infarction (tissue death due to lack of blood supply) in the area of distribution of the corticospinal tract can lead to hemiplegia. This is because the corticospinal tract is responsible for controlling voluntary movements, including those of the face, arm, and leg. Damage to this tract can result in weakness or paralysis of the affected side of the body.

**Why Each Wrong Option is Incorrect**
**Option A:** The anterior cerebral artery primarily supplies the medial surface of the brain, including the medial frontal lobe and the corpus callosum. Infarction in this area is more likely to result in personality changes, urinary incontinence, or weakness of the lower limbs, rather than hemiplegia.

**Option B:** The middle cerebral artery is the largest cerebral artery and supplies a significant portion of the lateral surface of the brain, including the motor cortex. However, infarction in this area can result in a range of symptoms, including hemiparesis (weakness of one side of the body), but not necessarily hemiplegia.

**Option C:** The posterior cerebral artery primarily supplies the occipital lobe and is involved in visual processing. Infarction in this area is more likely to result in visual disturbances, such as blindness or visual field defects, rather than hemiplegia.

**Clinical Pearl / High-Yield Fact**
The corticospinal tract is often affected in stroke patients, resulting in hemiplegia. It's essential to remember that the area of distribution of the corticospinal tract includes the motor cortex, the posterior limb of the internal capsule, the cerebral peduncles, and the lateral corticospinal tract.

**Correct Answer:** C. The middle cerebral artery is the most common cause of hemiplegia due to its extensive distribution to the motor cortex, which controls voluntary movements.