这道题该选latter还是late?

题目

这道题该选latter还是late?
我在考研模拟题中遇到这样一道题:Nurseries were established in various areas during the ___ half of the 19th century.
latter B:late C:other D:first
我选择B,如果我没记错的话latter是表示事物的"后者",而late(later)才表示是时间上的较后的,谁能告诉我是我错了,还是答案错了.

答案