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📰 But the question says "the node opposite to $O$", i.e., opposite the origin. That wording is misleading — $O$ is at the origin. But in the hexagon, the node farthest from $O$ is at $(-1, 0)$, which is at distance 1 — same as all others. But in a **regular hexagon**, all vertices are equidistant from center, so **no node is farther than others**. 📰 However, in a **scaled hexagonal lattice** used for energy grid modeling, nodes may be placed at **integer-coordinate projections** using vectors $\vec{v}_1 = (1, 0)$, $\vec{v}_2 = \left(\frac{1}{2}, \frac{\sqrt{3}}}{2}\right)$, but these are not integer. 📰 But the problem says "assuming integer coordinates are used in a scaled grid". So perhaps the hexagon is scaled by 2 to clear denominators: 📰 Unlock Hidden Beauty Crafted With A Mysterious Shell Necklace 4725494 📰 Wait The Lewis Dot Structure For Co Reveals A Shocking Secret Scientists Never Told You 824847 📰 Nasdaq Amzn Financials 9556970 📰 Curt Mills 5320902 📰 Fortnite Skins 7386635 📰 Clemson Acceptance Rate 8365304 📰 How To Obtain Financial Power Of Attorney 1727445 📰 Secrets From The Lincoln University Campus During The Deadly Mass Shooting 3896496 📰 New Netflix Shows Movies In 2024 That Are Taking Over Streaming Charts 4149207 📰 The Probability Of Drawing A Red Card From A Standard Deck Is Frac12 If Two Cards Are Drawn Without Replacement Find The Probability That Both Are Red 4692997 📰 B Technology Should Support Hands On Exploration And Visualization Of Abstract Concepts 4054328 📰 Kosten Der Ersten 500 Einheiten 1000 7826662 📰 Primark Indianapolis 6290619 📰 Squabble Up Lyrics Open Kendricks Darkest Secretslisten Untold 6019049 📰 The Shocking Truth About Zeldas Majoras Mask Revealedstunning Details Inside 1539818