1. The problem is to find the image of point $A=(-1,0)$ after reflection on the $y$-axis. 2. Reflection on the $y$-axis changes the $x$-coordinate of a point to its opposite, while the $y$-coordinate remains the same. 3. For point $A=(-1,0)$, the reflected point $A'$ will have coordinates: $$A' = ( -(-1), 0 ) = (1, 0)$$ 4. Therefore, the image of point $A$ after reflection on the $y$-axis is $A' = (1,0)$.