1 Use coordinate geometry to answer this question. Answers obtained from accurate drawing will receive no marks.
\(A\) and \(B\) are points with coordinates \(( - 1,4 )\) and \(( 7,8 )\) respectively.

1. Find the coordinates of the midpoint, M , of AB . Show also that the equation of the perpendicular bisector of AB is \(y + 2 x = 12\).
2. Find the area of the triangle bounded by the perpendicular bisector, the \(y\)-axis and the line AM , as sketched in Fig. 12. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{13979d37-ea09-4d51-aff8-81fa611cc080-1_449_873_843_856} \captionsetup{labelformat=empty} \caption{Fig. 12}
   \end{figure}