12 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.
- Find the coordinates of the midpoint, M , of AB .
Show also that the equation of the perpendicular bisector of AB is \(y + 2 x = 12\).
- 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]{7791371e-26d9-428c-8700-5121a1c6464a-4_451_483_776_790}
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\caption{Fig. 12}
\end{figure}
Not to scale