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1. A quadrilateral has vertices \(A(-4, -2)\), \(B(5, -1)\), \(C(6, 5)\) and \(D(-7, 6)\). Show that the mid-points of its sides form a parallelogram.
Mid point of \(AB\) \(=\) \(P\) \(=\)
Mid point of \(BC\) \(=\) \(Q\) \(=\)
Mid point of \(CD\) \(=\) \(R\) \(=\)
Mid point of \(DA\) \(=\) \(S\) \(=\)
Slope of \(PQ\) \(=\)
Slope of \(QR\) \(=\)
Slope of \(RS\) \(=\)
Slope of \(SP\) \(=\)
Thus, \(PQRS\) forms a parallelogram.
2. \(PQRS\) is a rhombus. Its diagonals \(PR\) and \(RS\) intersect at the point \(M\) and satisfy \(QS = 2PR\). If the coordinates of \(S\) and \(M\) are \((1, 1)\) and \((2, -1)\), respectively, find the coordinates of \(P\).
The coordinates of \(P\) \(=\) .
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