Coordinate Geometry - Midpoint of a Line Segment

Solutions to this question by accurate drawing will not be accepted.
The diagram shows a kite \(PQRS\). The two diagonals meet at \(M\). Given that the coordinates of the points \(P\), \(Q\), \(R\) and \(S\) are \(\left( -3,0 \right)\), \(\left( a,3 \right)\), \(\left( 5,2 \right)\) and \(\left( \frac{5}{2},\mathrm{ }-5 \right)\) respectively, where \(a\) is a constant, find

1. the coordinates of \(M\),
2. the equation of \(QS\).
3. Show that the value of \(a\) is \(\frac{1}{2}\).
4. Calculate the area of quadrilateral \(PQRS\).