10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9451ec48-d955-44a8-9988-68f7c0fb9821-14_541_863_287_541}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The points \(Q ( 1,3 )\) and \(R ( 7,0 )\) lie on the line \(l _ { 1 }\), as shown in Figure 2.
The length of \(Q R\) is \(a \sqrt { } 5\).
- Find the value of \(a\).
The line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\), passes through \(Q\) and crosses the \(y\)-axis at the point \(P\), as shown in Figure 2.
Find
- an equation for \(l _ { 2 }\),
- the coordinates of \(P\),
- the area of \(\triangle P Q R\).