2026 CSS P2 Q8

Solution to this question by accurate drawing is not accepted.

The diagram (not to scale) shows a right-angled triangle \(ABC\). \(A\) is the point \((4,6)\) and \(\angle ABC=90^\circ\). The equation of the line \(BC\) is \(y=\dfrac12x+2\).

Find

1. the equation of the line \(AB\),[2]
2. the coordinates of \(B\).[2]

\(Q\) lies on \(AB\) produced such that \(AB:BQ=2:3\).

3. Find the coordinates of \(Q\).[2]
4. Calculate the area of triangle \(ACQ\).[4]