Followed large coordinate in a tenacious way (8)
I believe the answer is:
doggedly
'in a tenacious way' is the definition.
(I know this)
'followed large coordinate' is the wordplay.
'followed' becomes 'dogged' (I've seen this before).
'large' becomes 'L' (eg in clothes sizes).
'coordinate' becomes 'Y' (as in X and Y coordinates on a grid).
'dogged'+'l'+'y'='DOGGEDLY'
(Other definitions for doggedly that I've seen before include "In a persistent manner" , "Persistently" , "With obstinate determination" .)