Gregor and his family are separated by doors throughout "The Metamorphosis." Explain what this shows about their relationship.

Well done for noticing this! Yes, it is clear that the way
that Gregor is "shut away" into his own room and how, at first, only his sister will
enter, and then, not even her, says something very profound about Gregor's standing in
the family. Their natural instinct upon discovering the true nature of Gregor's
transformation is to lock him away and keep him separate and isolated from themselves.
We are told that his parents in particular cannot even bring themselves to enter his
room during the first two weeks:

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During the first two weeks, the parents could not
get themselves to come into his room, and he often heard them expressing their great
appreciation of the sister's
efforts...

Of course, the way
in which Gregor is shut out from their world and the violence with which any
trangressions of this boundary are met, such as when his father bombards him with
apples, symbolises the way that Gregor is treated as an unwanted outcast, a figure that
his family do the best they can to ignore and pretend does not even exist. The real
question we have to ask ourselves though is whether this was the case before Gregor's
metamorphosis.