# Minimizing the Sum of Two Distances

Geometry Level 3

The value of $$y$$ that minimizes the sum of the two distances from $$(3,5)$$ to $$(1,y)$$ and from $$(1,y)$$ to $$(4,9)$$ can be written as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. Find $$a + b$$.

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