Final answer:
Samuel de Champlain was the explorer who mapped the New World's Atlantic coast from Cape Fear to Newfoundland and the bay of future New York. Option B is correct.
Step-by-step explanation:
The explorer who is recognized for mapping the New World's Atlantic coast from Cape Fear to Newfoundland, and the bay that would become New York, is Samuel de Champlain. Champlain was a French navigator and cartographer who in 1601 explored the Caribbean and the coast of New England.
Notably, in 1608, Samuel de Champlain founded Quebec, contributing significantly to the establishment of the French presence in the New World. Whereas explorers like Giovanni de Verrazano and Jacques Cartier were also critical to French explorations, it was de Champlain who extensively mapped the Atlantic coast and helped establish New France, which encompassed the area around the St. Lawrence Seaway.