Infinite variables exist. Replies to below will help:
What are respective crossover poles and rates:
HP?
LP?
If no HP state so. State whether you do or do not have HP crossover pole available for main speakers.
Describe main speaker:
Make/model?
Woofer complement?
Woofer loading? (sealed, reflex, direction port fires, etc)
Bass cutoff frequency, state unknown if unknown, state in-room or anechoic or unknown
Room dimensions (the physical universe comprises three dimensions so list three, two is as useless as one which is as useless as none)
Describe ceiling flat or no? If no, describe it, and state average height.
Describe sub: driver complement, amp power, loading, direction port fires, etc. Describe phase control; if none state so. Why do you care what direction the sub fires? Appearance? It seems odd to care about cosmetics with sub in the middle of the room. Placing a single sub can be extremely difficult and is likely the main reason audiophiles dislike single subs. Setup wrong they suck. The ideal location is least modal effects, which may well not be your described location.
AFTER you confirm pole questions above: confirm visually any location you might possibly locate the sub. I'll post as foolproof instructions as I've found to find the best location of all the locations you'd accept. Certainly, depending on the pole, there could be infinitely better location than mid point on the speaker plane.
Generally, the maximum permissible distance between (non distributed array) sub and main = 1/4 crossover pole wavelength. (Distributed Array voids this rule because it creates its own modal environment separate from the room's boundaries.)
FYI: L/R always and only refers to view from listening end.
