in Latin, the form of com- "together, with" in compounds with stems beginning in vowels, h-, and gn-; see com-. Taken in English from 17c. as a living prefix meaning "together, mutually, in common," and used promiscuously with native words (co-worker) and Latin-derived words not beginning with vowels (codependent), including some already having it (co-conspirator).
"lying in or otherwise related to a plane, flat," 1850, from Latin planaris "level, flat," from planum "plane" (from PIE root *pele- (2) "flat; to spread"). An earlier word in the same sense was planary (1660s).
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<a href="https://www.etymonline.com/word/coplanar">Etymology of coplanar by etymonline</a>
Harper, D. (n.d.). Etymology of coplanar. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/coplanar