Anna, keep at a distance FROM something or someone. -The large males kept at a distance from the rest of the herd, except during the mating season. -Extremely photosensitive individuals are advised to keep at a distance from TV screens. keep your distance from somebody or something. -She works in our office but she keeps her distance from the rest of us.

Neither is correct. He keeps his distance. He keeps a distance to everybody.

Neither of those sounds natural to me (American English). I think it's more common to say "keep s.o. at a distance." The person is a direct object rather than the obj. of the preposition.

If you see Eliot, keep your distance! He's a bad bad bad bad bad man! :D

Anna - it is so nice to see someone thank an answerer - and you are so polite, because you thank everyone. People will appreciate your good manners, and they will be glad that they tried to help answer your question.