The symplectic transvection group is isomorphic to what $A^1$, $A^2$?

Question

The transvections generate the symplectic group, but to demonstrate its connectedness I need to establish their connectedness. I was thinking of doing this through an isomorphism of alg. groups with $A^1$, but this seems wrong since I disregard t; but then if I take it with $A^2$ it is no longer an injection!!! In short, how do I establish the connectedness of each symplectic transvection group? Have I approached the problem incorrectly?