8. Midpoint

\(ABCD\) is a rectangle formed by the points \(A(-2, -2)\), \(B(-2, 4)\), \(C(5, 4)\) and \(D(5, -2)\). \(P\), \(Q\), \(R\) and \(S\) are mid-points of sides \(AB\), \(BC\), \(CD\) and \(DA\) respectively. Show that diagonals of the quadrilateral \(PQRS\) bisect each other. 

 

 

Midpoint of \(AB = P = \) $\left(i,i\right)$

 

Midpoint of \(BC = Q = \) $\left(i,i\right)$

 

Midpoint of \(CD = R = \) $\left(i,i\right)$

 

Midpoint of \(DA = S = \) $\left(i,i\right)$

 

Midpoint of \(PR\) \(=\) $\left(i,i\right)$

 

Midpoint of \(QS\) \(=\) $\left(i,i\right)$

 

Midpoint of \(PR\) =≠ Midpoint of \(QS\)

 

The diagonals of the quadrilateral \(PQRS\) do not bisect each otherbisect each other.