Higher November 2017 Paper 2 Q19
19 A triangle has vertices \(P\), \(Q\) and \(R\).
The coordinates of \(P\) are \((-3, -6)\)
The coordinates of \(Q\) are \((1, 4)\)
The coordinates of \(R\) are \((5, -2)\)
\(M\) is the midpoint of \(PQ\).
\(N\) is the midpoint of \(QR\).
Prove that \(MN\) is parallel to \(PR\).
You must show each stage of your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| Proof (supported) | M1 | for a method to find coordinates of \(M\,(-1, -1)\) or \(N\,(3, 1)\) |
| M1 | for method to find gradient of \(MN\) or \(PR\) or for method to find column vector for \(MN\) or \(PR\) or for differences of \(x\) coordinates and differences of \(y\) coordinates for \(MN\) or \(PR\) | |
| A1 | for gradients of \(MN\) and \(PR\), ie \(\frac{1}{2}\) oe or for column vectors of \(MN\) and \(PR\), \(\overrightarrow{MN} = \begin{pmatrix}4\\2\end{pmatrix}\) and \(\overrightarrow{PR} = \begin{pmatrix}8\\4\end{pmatrix}\) or for differences of \(x\) coordinates and of \(y\) coordinates for \(MN\) and \(PR\) | |
| C1 | for conclusion from reasoning and correct working |