Final answer:
During the late 19th century, Japan's rapid industrialization and military modernization allowed it to gain a significant advantage over China, culminating in a Japanese victory in the Sino-Japanese War, and resulting in the Treaty of Shimonoseki where China ceded territories to Japan.
Step-by-step explanation:
The relationship between China and Japan during the late 19th century is best described by rapid Japanese industrialization which allowed Japan to gain dominance over China. This was a time when China was experiencing a decline due to European imperialism, which had resulted in the partitioning of Chinese territory into various spheres of influence. By contrast, Japan had undergone significant modernization and was expanding its military and economic power.