Final answer:
Melantho is the character who has an affair with Eurymachus, according to Homer's epic poem, 'The Odyssey'.
Step-by-step explanation:
The character who has an affair with Eurymachus in the context of Greek mythology and literature is A) Melantho. Melantho is one of the maids in Odysseus's household who betrays Penelope by having a secret relationship with one of the suitors, Eurymachus. This incident is part of the narrative in Homer's epic poem, 'The Odyssey'. Melantho's disloyalty contrasts greatly with Penelope's steadfastness and virtue as she waits years for her husband's return from the Trojan War.