6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e6a4beaa-2c1f-4a98-bc63-4ddb8611db45-12_650_885_255_603}
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\caption{Figure 2}
\end{figure}
The straight line \(l _ { 1 }\) has equation \(2 y = 3 x + 7\)
The line \(l _ { 1 }\) crosses the \(y\)-axis at the point \(A\) as shown in Figure 2.
- State the gradient of \(l _ { 1 }\)
- Write down the coordinates of the point \(A\).
Another straight line \(l _ { 2 }\) intersects \(l _ { 1 }\) at the point \(B ( 1,5 )\) and crosses the \(x\)-axis at the point \(C\), as shown in Figure 2.
Given that \(\angle A B C = 90 ^ { \circ }\),
- find an equation of \(l _ { 2 }\) in the form \(a x + b y + c = 0\), where \(a\), b and \(c\) are integers.
The rectangle \(A B C D\), shown shaded in Figure 2, has vertices at the points \(A , B , C\) and \(D\).
- Find the exact area of rectangle \(A B C D\).