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2019 AMC 10BProblem 4P1-10~2 minPrint
Coordinate GeometrySequences & SeriesSet up the equation/formula and compute; no special trick neededTest small/specific values or special cases to find or verify the answer

All lines with equation ax+by=cax+by=c such that a,b,ca,b,c form an arithmetic progression pass through a common point. What are the coordinates of that point?

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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.