A geometry problem by Soumava Pal

Geometry Level 3

A triangle with vertices \(A,B,C\) with coordinates \(\left(2,\frac{1}{2}\right)\), \(\left(4,\frac{1}{4}\right)\), \(\left(3,\frac{1}{3}\right)\) has orthocentre at \(H=(x,y)\).

Find y.

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