2025 IGCSE 0580 May/June P21 Q21

2025 IGCSE 0580 May/June P21 Q21

5 marks

\(OABC\) is a rhombus and \(O\) is the origin.

The diagonals of the rhombus intersect at \(P\).

\(\overrightarrow{OP}=2\mathbf{m}\) and \(\overrightarrow{AP}=\mathbf{n}\).

  1. Find, in terms of \(\mathbf{m}\) and \(\mathbf{n}\), in its simplest form
    1. \(\overrightarrow{OA}\)[1]
    2. \(\overrightarrow{OC}\).[1]
  2. \(D\) is the point such that \(\overrightarrow{AD}=10\mathbf{m}-3\mathbf{n}\).
    Show that \(OADC\) is a trapezium.[3]

Solution:

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Answer:(a)(i) \(2\mathbf{m}-\mathbf{n}\). (ii) \(2\mathbf{m}+\mathbf{n}\). (b) \(\overrightarrow{CD}=5\overrightarrow{OA}\), so \(CD\parallel OA\) and \(OADC\) is a trapezium.

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