8.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{bace07ee-1eb8-43d6-8229-152d1f74ab59-14_687_1196_280_388}
\end{figure}
The points \(A ( 1,7 ) , B ( 20,7 )\) and \(C ( p , q )\) form the vertices of a triangle \(A B C\), as shown in Figure 2. The point \(D ( 8,2 )\) is the mid-point of \(A C\).
- Find the value of \(p\) and the value of \(q\).
The line \(l\), which passes through \(D\) and is perpendicular to \(A C\), intersects \(A B\) at \(E\).
- Find an equation for \(l\), in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
- Find the exact \(x\)-coordinate of \(E\).