Under the influence of drugs, either prescribed medicines or illegal drugs, causing drowsiness or altered awareness.
From 'drug' (origin uncertain, possibly from French 'drogue'), with '-ed' suffix making it an adjective. The word 'drug' itself has mysterious roots, suggesting exotic or unusual substances.
It's striking that we use one word 'drugged' for both prescription medication effects and poisoning—the word doesn't distinguish between helpful medicine and harmful substances, just the state of being affected.
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