h₃reǵ-tó-
“straightened, directed, right”Source of Latin rēctus, English right, correct, direct, erect
Past participle of the rule root, yielding Latin rēctus and English right, correct, direct, erect.
Discussion
The PIE form *h₃reǵ-tó- (made straight, directed, correct) is a past participle from *h₃reǵ- (to straighten, to direct), meaning "that which has been straightened" — hence right, correct, proper.
English right (OE riht, from PGmc *rehtaz) descends directly from this form. The word carries the full semantic range of the PIE concept: morally right (correct, proper), directionally right (the opposite of left), legally right (a right, an entitlement), and geometrically right (a right angle — an angle that is straight/correct). All four senses derive from the single PIE image of straightness.
Latin rēctus (straight, upright, correct — the past participle of regere) gave English: rector (one who keeps things straight), rectify (to make straight/correct), correct (con-rēctus, thoroughly straightened), erect (ē-rēctus, straightened up), direct (dī-rēctus, straightened apart), and rectangle (a straight-angled figure).
The connection between straightness and morality is not uniquely IE — many cultures equate the straight path with the good path — but PIE encoded it lexically with unusual thoroughness. The same root that names the king (*h₃reǵ-s) names the concept of rightness (*h₃reǵ-tó-) and the act of ruling (*h₃reǵ- base verb). To rule, to be right, and to be king are etymologically the same gesture: keeping the line straight.
German recht (right, correct, law) and Dutch recht confirm the pan-Germanic distribution. The word Recht in German means both "right" (entitlement) and "law" — the same conflation found in English.