Final answer:
The plot concerning the murder of Agnes Botherwood and the policeman solving it falls under the detective story or mystery genre, which is characterized by a crime, a criminal, and a detective working to solve the case.
Step-by-step explanation:
The question you have asked refers to the genre of a story in which a policeman is tasked with solving a murder. As described by the plot beginning, this type of story falls within the detective story or mystery genre. According to the literary references provided, detective stories contain specific elements such as a crime (usually a murder, in this case, of Agnes Botherwood), a criminal, and a detective or sleuth who attempts to solve the crime.
Additional aspects such as the examination of a hero, trickery, genre categorizations, and noteworthy writers like Edgar Allan Poe and Mary Shelley, who contributed to the gothic and mystery genres, provide context and depth to the discussion on literary genres.