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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