down the middle or across

[Barbara Need]

I have just seen a Jif Peanut Butter commercial for the umpteenth
time in which a little girl, having made a peanut butter sandwich to
share with her friend on a sleep over, asks if her mother cuts it
"down the middle or across". The answer is across and the sandwich is
cut diagonally. For me, at best, these two directions would be
perpendicular, that is vertically or horizontally (if you can picture
this). Does anyone else have the diagonal interpretation?

Barbara