Final answer:
Penelope tests Odysseus by challenging him to move their bed, which she knows to be impossible. When he reacts with the knowledge that the bed cannot be moved as it is rooted to a living olive tree, Penelope's doubts are dispelled and she explains her coldness as necessary caution.
Step-by-step explanation:
In Homer's epic poem The Odyssey, Penelope tests Odysseus to ensure he is truly her husband by asking him to move their bed. However, he knows that this is impossible, as one of the bed's legs is a living olive tree, which he built the room around. Upon his correct response that such a task can't be done, Penelope is satisfied that the stranger before her is indeed her long-lost husband, as only the real Odysseus would know this secret about their bed. She explains her seeming coldness was due to her need to be cautious and to be sure of his identity before revealing her emotions, given the many suitors who lied and deceived in their quest to marry her.