Moderate -0.3 This is a standard coordinate geometry question requiring finding equations of lines using parallel/perpendicular conditions, then solving simultaneous equations. It involves multiple routine steps (gradient of OB, gradient perpendicular to AB, two line equations, intersection) but each step uses well-practiced techniques with no novel insight required. Slightly easier than average due to being purely procedural.
\includegraphics{figure_4}
In the diagram, \(A\) is the point \((-1, 3)\) and \(B\) is the point \((3, 1)\). The line \(L_1\) passes through \(A\) and is parallel to \(OB\). The line \(L_2\) passes through \(B\) and is perpendicular to \(AB\). The lines \(L_1\) and \(L_2\) meet at \(C\). Find the coordinates of \(C\). [6]
\includegraphics{figure_4}
In the diagram, $A$ is the point $(-1, 3)$ and $B$ is the point $(3, 1)$. The line $L_1$ passes through $A$ and is parallel to $OB$. The line $L_2$ passes through $B$ and is perpendicular to $AB$. The lines $L_1$ and $L_2$ meet at $C$. Find the coordinates of $C$. [6]
\hfill \mbox{\textit{CAIE P1 2010 Q4 [6]}}