The correct verb to be used in the sentence will be, “They wanted to build a holiday resort here, but the owners of those beachfront cottages 'refused' to play ball.”
A verb is a form of a word or a phrase that expresses the continuity of an action in the sentence. There are two types of verbs, main verb and the auxiliary verb.
When 'refused' verb is used in the sentence, it expresses the correct grammatical structure of the sentence. Thus, the word “refused” is the correct verb being used.
Hence, option A holds true regarding the correct verb.
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