Step 1: Understanding Prepositions of Position:
The preposition "against" is used when one object is in contact with and supported by another. The ladder is leaning against the wall.
Step 2: Analyzing the Options:
- Against: The correct preposition, indicating that the ladder is leaning on the wall.
- For: Incorrect, as "for" is used to indicate purpose or reason, not position.
- At: Incorrect, as "at" is used for specific points or locations, not for leaning or support.
- In: Incorrect, as "in" suggests being inside something, not leaning on it.
Step 3: Conclusion:
The correct preposition is against, indicating that the ladder is leaning on the wall.