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The diagram shows a rhombus \(A B C D\) in which the point \(A\) is ( \(- 1,2\) ), the point \(C\) is ( 5,4 ) and the point \(B\) lies on the \(y\)-axis. Find
- the equation of the perpendicular bisector of \(A C\),
- the coordinates of \(B\) and \(D\),
- the area of the rhombus.