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locus of points symmetric to M wrt PQ so that <PMQ is right, Q in x'x, P in y'y

Source: Sharygin 2011 Final 8.7

December 15, 2018
geometryLocusLocus problemsright angleaxes

Problem Statement

Let a point MM not lying on coordinates axes be given. Points QQ and PP move along YY - and XX-axis respectively so that angle PMQP M Q is always right. Find the locus of points symmetric to MM wrt PQP Q.
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