2 Fig. 2 shows the unit square, OABC , and its image, $\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }$, after undergoing a transformation.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{3df020b0-fb7b-454b-b354-36cc2b8df5f6-2_595_739_571_664}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}

(i) Write down the matrix $\mathbf { T }$ representing this transformation.

The quadrilateral $\mathrm { OA } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }$ is reflected in the $x$-axis to give a new quadrilateral, $\mathrm { OA } ^ { \prime \prime } \mathrm { B } ^ { \prime \prime } \mathrm { C } ^ { \prime \prime }$.\\
(ii) Write down the matrix representing reflection in the $x$-axis.\\
(iii) Find the single matrix that will transform OABC onto $\mathrm { OA } ^ { \prime \prime } \mathrm { B } ^ { \prime \prime } \mathrm { C } ^ { \prime \prime }$.

\hfill \mbox{\textit{OCR MEI FP1 2014 Q2 [5]}}