In the historical context of "Where is Qin when sending Zhu Da to Qin?", the concise answer is that Qin was located in the central plains of what is now modern-day China. This region, known as the Yellow River basin, was the heartland of the Qin Dynasty during the Warring States period. Zhu Da, a prominent figure in the story, was sent to Qin to serve as a vassal king, which indicates that Qin was a powerful and influential state at the time.

The Qin Dynasty, established by Qin Shi Huang in 221 BCE, was known for its centralized authority and the implementation of legalist principles. The central plains, where Qin was based, were strategically advantageous due to their fertile land and access to trade routes. This location allowed Qin to expand its influence and eventually conquer the other Warring States, unifying China for the first time.

Historical records, such as the "Records of the Grand Historian" by Sima Qian, provide insights into the geographical and political landscape of the time. According to Sima Qian, Qin was situated in the region that is now part of Shaanxi Province, with its capital at Xianyang. This area was characterized by its central location, which facilitated communication and control over the vast territories that Qin sought to conquer.

The strategic importance of the central plains is further evidenced by the fact that Qin Shi Huang initiated massive infrastructure projects, such as the construction of the Great Wall and the Terracotta Army, to defend and expand his empire. These projects were only feasible due to the logistical advantages of the central plains.

In conclusion, Qin was located in the central plains of modern-day China during the time of Zhu Da's mission, which was a pivotal period in the unification of China. The geographical and political significance of this region, as documented in historical texts, underscores the strategic importance of Qin's location and its role in the subsequent history of China.