10
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b927f8b-ddf8-481d-a1ce-3b90bb1435f0-3_437_572_1058_538}
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\caption{Fig. 10}
\end{figure}
In Fig.10, A has coordinates \(( 1,1 )\) and C has coordinates \(( 3,5 )\). M is the mid-point of AC . The line \(l\) is perpendicular to AC.
- Find the coordinates of M .
Hence find the equation of \(l\).
- The point B has coordinates \(( - 2,5 )\).
Show that B lies on the line \(l\).
Find the coordinates of the point D such that ABCD is a rhombus. - Find the lengths MC and MB .
Hence calculate the area of the rhombus ABCD .