Question

1.the police found a clue at murder. (to/at/for).​

Answer 1

Answer:

the police found the clue to the murder

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Answer 2

The most appropriate option to be used with the word 'clue' is 'to'.

Explanation

'Clue' means an object, a piece of evidence or some information that helps the police solve a crime.

The convention or rule is with the word 'clue' we usually use the preposition 'to'.  

If any other preposition is used, it will be inappropriate; as a language is nothing but a collection of rules and lingual conventions that all have to adhere to.