The correct answer is the Epiphyseal plate.

- The epiphyseal plate, also known as the growth plate, is a layer of hyaline cartilage found at the ends of long bones in children and adolescents.
- This region is responsible for the longitudinal growth of bones during development.
- The process occurs through endochondral ossification, where cartilage cells (chondrocytes) divide and enlarge, then are gradually replaced by bone tissue, resulting in an increase in the length of the bone.

Key points:
- The Diaphysis is the shaft or central part of a long bone, primarily involved in providing structural support, not growth in length.
- The Periosteum is a dense layer of vascular connective tissue enveloping the bones except at the surfaces of the joints, playing a role in bone thickness and repair, but not longitudinal growth.
- The Medullary cavity is the central cavity where bone marrow is housed; it does not participate in elongation of bones.

Reference: Gray's Anatomy, 41st Edition, Chapter 6: The Skeleton - Bone Growth and Development, p. 112