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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.