Why did persues kill polydectes?

Perseus killed Polydectes because the king had been plotting to marry his mother, Danaë, against her will. Polydectes had also tricked Perseus into taking on a dangerous quest to retrieve the head of Medusa, hoping to eliminate him in the process. Upon returning victorious, Perseus used Medusa's head to turn Polydectes and his followers to stone, ultimately freeing his mother from the king's unwanted advances.