Interrogate
late 15th century: from Latin interrogat- ‘questioned’, from the verb interrogare, from inter- ‘between’ + rogare ‘ask’.
wiktionary
From Latin interrogātus, past participle of interrogāre(“to ask, question”), from inter(“between”) + rogāre(“to ask”); see rogation.
etymonline
interrogate (v.)
late 15c., a back-formation from interrogation or else from Latin interrogatus, past participle of interrogare "to ask, question, inquire; interrogate judicially, cross-examine," from inter "between" (see inter-) + rogare "to ask, to question," apparently a figurative use of a PIE verb meaning literally "to stretch out (the hand)," from root *reg- "move in a straight line." The Old French word was interroger (14c.) which yielded English interroge (late 15c.), now obsolete. Related: Interrogated; interrogating.