Not dilated at 38+4

Hi all,

I’m kinda worried. I’m 38+4 and measuring 39 weeks. I am only 1cm dilated. This is my first. My due date is may 5. I was told if I wasn’t dilated more by next Wednesday (39+4) they would schedule an induction sometime after my due date. Two questions:

-how far out do they usually schedule inductions? Like it wouldn’t be more than a week past my due date right?

-anyone on here have experience not being dilated at all at this point and give birth by their due date?

Edit: I THINK the reason why they mentioned induction was because I am measuring ahead and they’re just wanting to factor in baby’s size.