0606 P11 - Nov 2021 - Q2 - 6 marks
8010
Points \(A\) and \(C\) have coordinates \((-4,6)\) and \((2,18)\) respectively. The point \(B\) lies on the line \(AC\) such that \(\overrightarrow{AB}=\frac23\overrightarrow{AC}\).
(a) Find the coordinates of \(B\).
(b) Find the equation of the line \(l\), which is perpendicular to \(AC\) and passes through \(B\).
(c) Find the area enclosed by the line \(l\) and the coordinate axes.
