Cut a square without a corner with legs length $a/2$, $a/2$ into two equal pieces with just one line?

Question

This got me wondering on a friends party, where my friend ate the corner of the cake and my other friend and I wanted to share the leftover cake. I know how to do it in 3 cuts, by cutting the diagonal then cutting a corner with the same area off and then cut that corner in half, but how do I do it in 1 line?

Answer 1

Cut along the line connecting the NW corner to where the SE corner was before your first friend ate it.