1MA0 Higher June 2014 Paper 1 Q24
*24
Diagram NOT accurately drawn
\(OAB\) is a triangle.
\(M\) is the midpoint of \(OA\).
\(N\) is the midpoint of \(OB\).
\(\overrightarrow{OM} = \mathbf{m}\)
\(\overrightarrow{ON} = \mathbf{n}\)
Show that \(AB\) is parallel to \(MN\). (3)
| Answer | Mark | Notes |
|---|---|---|
| Proof | 3 | M1 for \(\overrightarrow{MN} = \overrightarrow{MO} + \overrightarrow{ON}\) \((= \mathbf{n} - \mathbf{m})\) or \(\overrightarrow{NM} = \overrightarrow{OM} + \overrightarrow{NO}\) \((= \mathbf{m} - \mathbf{n})\) or \(\overrightarrow{AB} = \overrightarrow{AO} + \overrightarrow{OB}\) \((= 2\mathbf{n} - 2\mathbf{m})\) or \(\overrightarrow{BA} = \overrightarrow{OA} + \overrightarrow{BO}\) \((= 2\mathbf{m} - 2\mathbf{n})\) M1 for \(\overrightarrow{MN} = \mathbf{n} - \mathbf{m}\) and \(\overrightarrow{AB} = 2\mathbf{n} - 2\mathbf{m}\) oe C1 (dep on M1, M1) for fully correct proof, with \(\overrightarrow{AB} = 2\overrightarrow{MN}\) or \(AB\) is a multiple of \(\overrightarrow{MN}\) [SC M1 for \(\overrightarrow{MN} = 0.5\mathbf{n} - 0.5\mathbf{m}\) and \(\overrightarrow{AB} = \mathbf{n} - \mathbf{m}\) C1 (dep on M1) for fully correct proof, with \(\overrightarrow{AB} = 2\overrightarrow{MN}\) or \(AB\) is a multiple of of \(\overrightarrow{MN}\)] |