Solution
= Solution
Translate the mirror line to zero, reflect there, then translate back. Under the column-vector convention the rightmost operation acts first:
$$
\boxed{T(2,0)JT(-2,0)=\begin{pmatrix}-1&0&4\\0&1&0\\0&0&1\end{pmatrix}.}
$$
This <composition of affine transformations> maps $(x,y)$ to $(4-x,y)$, fixing exactly the points with $x=2$.