Coordinate Geometry - Midpoint of a Line Segment

Coordinate Geometry - Midpoint of a Line Segment

Solutions to this question by accurate drawing will not be accepted.
\(PQRS\) is a kite such that the coordinates of \(Q\) and \(S\) are \(\left( 3,6 \right)\) and \(\left( -1,4 \right)\) respectively.
Given that \(P\) lies on the \(y\)-axis and \(R\) lies on the \(x\)-axis, find the

  1. coordinates of \(M\), the midpoint of \(QS\).
  2. equation of the perpendicular bisector of \(QS\).
  3. coordinates of \(P\) and \(R\).
  4. area of the kite \(PQRS\).

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Answer:(a) \(M=(1,5)\) (b) \(y=-2x+7\) (c) \(P=(0,7)\), \(R=\left(\frac72,0\right)\) (d) \(\frac{35}{2}\text{ units}^2\)

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