Final answer:
Daedalus and Icarus were imprisoned because they were trying to escape from the king's labyrinth after Daedalus built it to contain the Minotaur, and they wanted to prevent the spread of its secrets.
Step-by-step explanation:
Daedalus and Icarus were imprisoned on the island because they were trying to escape from the king's labyrinth. Daedalus, a skilled craftsman, created the labyrinth on the island of Crete to house the Minotaur, a mythical creature that was half man and half bull. However, Daedalus and his son Icarus became prisoners of King Minos to prevent them from revealing the secrets of the labyrinth. In an attempt to escape, Daedalus crafted two sets of wings made of feathers and wax for himself and Icarus. Tragically, despite Daedalus's warnings to not fly too close to the sun, Icarus soared too high, causing his wings to melt and leading to his downfall into the sea.