10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb1becd5-96c1-426d-9b85-4bbc4a61af27-24_863_929_255_511}
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\caption{Figure 4}
\end{figure}
Diagram NOT drawn to scale
The points \(A ( 7 , - 3 ) , B ( 7,20 )\) and \(C ( p , q )\) form the vertices of a triangle \(A B C\), as shown in Figure 4. The point \(D ( 10,5 )\) is the midpoint of \(A C\).
- Find the value of \(p\) and the value of \(q\).
The line \(l\) passes through \(D\) and is perpendicular to \(A C\).
- Find an equation for \(l\), in the form \(a x + b y = c\), where \(a\), \(b\) and \(c\) are integers.
Given that the line \(l\) intersects \(A B\) at \(E\),
- find the exact coordinates of \(E\).