3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2033889-3cc5-48de-9bdb-cb1861921a2a-05_702_700_278_712}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 is a sketch showing the line \(l _ { 1 }\) with equation \(y = 2 x - 1\) and the point \(A\) with coordinates \(( - 2,3 )\).
The line \(l _ { 2 }\) passes through \(A\) and is perpendicular to \(l _ { 1 }\)
- Find the equation of \(l _ { 2 }\) writing your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found.
The point \(B\) and the point \(C\) lie on \(l _ { 1 }\) such that \(A B C\) is an isosceles triangle with \(A B = A C = 2 \sqrt { 13 }\)
- Show that the \(x\) coordinates of points \(B\) and \(C\) satisfy the equation
$$5 x ^ { 2 } - 12 x - 32 = 0$$
Given that \(B\) lies in the 3rd quadrant
- find, using algebra and showing your working, the coordinates of \(B\).