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2003 AMC 12A Problem 9

Problem 9 of 25EasierGeometry

A set SS of points in the xyxy-plane is symmetric about the origin, both coordinate axes, and the line y=x.y = x. If (2,3)(2, 3) is in S,S, what is the smallest number of points in S?S?

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Solution

Reflecting across y=xy=x gives (3,2),(3,2), and reflecting across the axes gives all points (±2,±3)(\pm2,\pm3) and (±3,±2).(\pm3,\pm2). There are 88 such points, and this set is already symmetric about the origin, both axes, and y=x.y=x. Thus, the correct answer is D.

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Concepts: transformation · symmetry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.