In the late 1800s, which of these rights was enjoyed by women in some parts
of the west but generally not by women on the east coast?

In 1800s women in the west enjoyed their right to suffrage, unlike  women who live in the East. It became an attraction to women to live in the west, but in the East, they have to fight for their right to suffrage.

It was said that women in the West enjoyed this right, however, it was a strategy to add more women in their population since there was a low population of women in the West. 

the scientific revolution brought us a renewed understanding of humanity and our place in the universe, new scientific equipment, and new laws as a basis for future scientific discovery.

c. extended rights of citizenship to new groups