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**. - Portal da Acústica