In describing the coats, which word correctly fills the blank?

The word that correctly fills the blank in the context of describing the coats is "on." This preposition is used to indicate that something is placed upon a surface or is in contact with it. When talking about coats, one might say "the coats are on the rack," which indicates their position relative to the rack.

Using "on" emphasizes the immediate location or the surface where the coats are situated, which is appropriate when describing how or where items are placed. It also aligns with common English usage, where "on" is often the preferred choice for items that are not enclosed but rather laid over or resting atop something else.

The other prepositions do not fit as naturally in this context. "At" would suggest a general location but lacks the specific relationship that "on" conveys. "In" indicates being enclosed within something and would not be suitable for coats that are typically hung or placed over a surface. "By" can imply proximity but does not convey the same meaning of placement as "on." Thus, "on" is the most fitting word in this scenario.