I'm sure his has a general form and welcome a link to a duplicate, but as I don't quite know what to search for, here goes.
Whilst answering a question on the Mathematics Stack Exchange, I found myself needing to say the mid point of one diagonal of a rectangle is coincidental with the mid point of the other and that that point is the centre of the rectangle. So I said:
"The key is to prove that for all rectangles, the mid points of the diagonals are coincidental at the centre of the rectangle ..."
It suddenly struck me that the correct form might have been:
"The key is to prove that for all rectangles, the mid point of the diagonals are coincidental at the centre of the rectangle ..."
I suspect this is related to "everyone took off his hat".
Could someone explain the reasoning behind the correct form.