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2023 AMC 10AProblem 19P16-20~5 minPrint
Coordinate GeometryTransformations & SymmetryAdd construction lines/points (drop altitudes, extend segments, connect centers)Set up the equation/formula and compute; no special trick needed

The line segment formed by A(1,2)A(1, 2) and B(3,3)B(3, 3) is rotated to the line segment formed by A′(3,1)A'(3, 1) and B′(4,3)B'(4, 3) about the point P(r,s)P(r, s) . What is ∣r−s∣|r-s| ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.