9 Simplify \(( n + 3 ) ^ { 2 } - n ^ { 2 }\). Hence explain why, when \(n\) is an integer, \(( n + 3 ) ^ { 2 } - n ^ { 2 }\) is never an even number. Given also that \(( n + 3 ) ^ { 2 } - n ^ { 2 }\) is divisible by 9 , what can you say about \(n\) ?
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0088b5e7-d587-419a-a13b-87527ac658c4-3_442_762_379_648}
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\caption{Fig. 10}
\end{figure}
Fig. 10 is a sketch of quadrilateral ABCD with vertices \(\mathrm { A } ( 1,5 ) , \mathrm { B } ( - 1,1 ) , \mathrm { C } ( 3 , - 1 )\) and \(\mathrm { D } ( 11,5 )\).
- Show that \(\mathrm { AB } = \mathrm { BC }\).
- Show that the diagonals AC and BD are perpendicular.
- Find the midpoint of AC . Show that BD bisects AC but AC does not bisect BD .