Why Is the Electric Flux from a Point Charge Only Half Through the XY Plane?

[Hammed]

A point charge +Q is located 1 m below the x-y plane. What is the total electric flux passing through the x-y plane? I know the answer should be Q/2 but how?

 

[Doc Al]

Imagine field lines emanating radially from that point charge. Which field lines will cross that plane? Which will never make it to that plane?

 

[haruspex]

A point charge +Q is located 1 m below the x-y plane. What is the total electric flux passing through the x-y plane? I know the answer should be Q/2 but how?

How will the flux lines be arranged around the charge? What symmetry is there?