3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b85f4635-aa93-4c6a-9d1f-2ef5bac1b48c-02_650_1043_367_317}
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\caption{Fig. 2}
\end{figure}
The points \(A ( 3,0 )\) and \(B ( 0,4 )\) are two vertices of the rectangle \(A B C D\), as shown in Fig. 2.
- Write down the gradient of \(A B\) and hence the gradient of \(B C\).
The point \(C\) has coordinates \(( 8 , k )\), where \(k\) is a positive constant.
- Find the length of \(B C\) in terms of \(k\).
Given that the length of \(B C\) is 10 and using your answer to part (b),
- find the value of \(k\),
- find the coordinates of \(D\).