I do not think this is a DIY problem. I would hire a plasterer. Not a painter who does plastering. A specialist in plastering only. They can be costly, but in this case a good idea. You should be able to get such a person to come and give you a free estimate. With a trained eye, s/he can tell you in a minute how serious that crack is, and what you need to do about it.

I think you need a drywall contractor rather than a plasterer. I think that's what haus meant to say.

If there is insulation above the drywall ceiling, it could get complicated just trying to screw it back up there. Do you know what's up there?

It seems unlikely that they just forgot to put screws or nails in that section. If the house is that old it would have come down long ago.

Have a professional look at it. Many years ago a neighbor had her dining room ceiling cave in....Bottom line. There was a small fire in the house prior to her buying it and the timbers/rafters had damage due to the fire and eventually gave way causing the ceiling to fall in. Unless you are the original owner, you never know what occurred prior to you buying the house.

when we remodeled and removed the ceiling in our master b/r
my husband showed me the joists were eaten through by termites. That would certainly cause the ceiling to bow as it would no longer be supported. Those joists are 18 inches on center.

Your home might be 35 years old but how long have YOU owned it?

If you are the new owner you have no idea if the previous owner used enough screws. If that is the case I would put screws in the joists to hold up the ceiling and investigate why the ceiling was replaced to begin with.