8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2217be5e-8edd-413f-9c97-212e585ff58d-16_769_979_269_479}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The line \(l _ { 1 }\), shown in Figure 2 has equation \(2 x + 3 y = 26\)
The line \(l _ { 2 }\) passes through the origin \(O\) and is perpendicular to \(l _ { 1 }\)
- Find an equation for the line \(l _ { 2 }\)
The line \(l _ { 2 }\) intersects the line \(l _ { 1 }\) at the point \(C\). Line \(l _ { 1 }\) crosses the \(y\)-axis at the point \(B\) as shown in Figure 2.
- Find the area of triangle \(O B C\). Give your answer in the form \(\frac { a } { b }\), where \(a\) and \(b\) are integers to be found.
a) \(L _ { 1 } : 2 x + 3 y = 26\)
\includegraphics[max width=\textwidth, alt={}, center]{2217be5e-8edd-413f-9c97-212e585ff58d-16_188_820_2039_159}
\includegraphics[max width=\textwidth, alt={}, center]{2217be5e-8edd-413f-9c97-212e585ff58d-16_129_631_2268_468}
$$\begin{gathered}
y = 3 / 2 x + 0
y = 3 / 2 x
\end{gathered}$$
\includegraphics[max width=\textwidth, alt={}, center]{2217be5e-8edd-413f-9c97-212e585ff58d-17_2257_51_315_34}
b) \(A = \frac { 6 x h } { 2 } \quad L _ { 1 } : 2 x + 3 y = 26\)
$$L _ { 2 } : y = 3 / 2 x$$
At B: \(x = 0 : 0 + 3 y = 26 y = 26 / 3\)
At C: \(2 x + 3 \left( \frac { 3 x } { 2 } \right) = 26\)
\(\therefore x = 4\)
\(A = \frac { 4 \times 26 } { 3 } = 52 / 3\)
| VIAV SIHI NI IIIIM IONOO | VIIV SIHI NI JIIIM ION OC | VEYV SIHI NI JIIYM ION OO |
\includegraphics[max width=\textwidth, alt={}]{2217be5e-8edd-413f-9c97-212e585ff58d-19_2255_54_312_34}
\includegraphics[max width=\textwidth, alt={}, center]{2217be5e-8edd-413f-9c97-212e585ff58d-19_113_61_2604_1884}