**Core Concept**
Hesselbach's triangle is an anatomical region in the anterior abdominal wall, significant in the context of hernia formation and repair. It is a critical concept in surgical anatomy, particularly in the diagnosis and management of inguinal hernias.

**Why the Correct Answer is Right**
The linea semilunaris, also known as the semilunar line, serves as the medial border of Hesselbach's triangle. This line marks the lateral margin of the rectus sheath and separates the rectus abdominis muscle from the external oblique muscle. The linea semilunaris is a key anatomical landmark in the anterior abdominal wall, and its identification is essential for understanding the boundaries of Hesselbach's triangle. The correct identification of the linea semilunaris as the medial border of Hesselbach's triangle is crucial for accurate diagnosis and surgical planning.

**Why Each Wrong Option is Incorrect**
**Option A:** The linea alba, which is the fibrous structure running along the midline of the abdomen, does not form the medial border of Hesselbach's triangle. It is actually the lateral border of the rectus sheath that is formed by the linea semilunaris.
**Option C:** The inferior epigastric artery is a significant structure in the anterior abdominal wall, but it does not form the medial border of Hesselbach's triangle. It is actually located within the rectus sheath and runs along the posterior surface of the rectus abdominis muscle.
**Option D:** The conjoint tendon, which is formed by the aponeuroses of the internal oblique and transversus abdominis muscles, does not form the medial border of Hesselbach's triangle. It is actually the lateral border of Hesselbach's triangle.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the boundaries of Hesselbach's triangle are critical for the diagnosis and management of inguinal hernias. A thorough understanding of the anatomy of this region is necessary for accurate surgical planning and execution.

**✓ Correct Answer: B. Linea semilunaris**