Answer
$BZ=\left[ \begin{matrix}
x \\
-y \\
\end{matrix} \right]$ and the $x$ coordinate is the same but the $y$ coordinate is changed by $-y$. Thus, its
graphic reflection is about the $x-\text{axis}$.
Work Step by Step
Perform matrix multiplication in order to find $BZ$ as below.
$\begin{align}
& BZ=\text{ }\left[ \begin{matrix}
1 & 0 \\
0 & -1 \\
\end{matrix} \right]\text{ }\left[ \begin{matrix}
x \\
y \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
1\cdot x+0\cdot y \\
0\cdot x-1\cdot y \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
x \\
-y \\
\end{matrix} \right]
\end{align}$
It can be observed that in $BZ$, the $x$ coordinate is the same but the $y$ coordinate is changed by $-y$. Thus, its graphic reflection is about the $x-\text{axis}$.
