Final answer:
The design year of the Dry Garden Ryoan-ji in Kyoto, Japan most closely corresponds to the year 1) 1450, well before the Edo period, making it the correct answer.
Step-by-step explanation:
The current design year of the Dry Garden Ryoan-ji in Kyoto, Japan, dates back to before the Edo period, which suggests that only the first two options, 1450 and 1750, could potentially be correct.
Given that Utagawa Hiroshige, an artist from the Edo period, created art depicting scenes from travel along the Tōkaidō road, which was well before 1950, 1850 is too late to be part of the formative period of the garden.
Therefore, the correct answer is 1) 1450.