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 \(a + b\).