0606 P21 - Jun 2019 - Q10 - 8 marks
8294
The points \(A\) and \(B\) have coordinates \((p,3)\) and \((1,4)\) respectively, and the line \(L\) has equation \(3x+y=2\).
(i) Given that the gradient of \(AB\) is \(\frac13\), find \(p\).
(ii) Show that \(L\) is the perpendicular bisector of \(AB\).
(iii) Given that \(C(q,-10)\) lies on \(L\), find \(q\).
(iv) Find the area of triangle \(ABC\).
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