November 2021 Paper 2 Q14
14
(a) \(\mathbf{A} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\)
Describe geometrically the single transformation represented by \(\mathbf{A}\). [1 mark]
(b) \(\mathbf{B} = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\)
Describe geometrically the single transformation represented by \(\mathbf{B}^2\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Reflection in the \(x\)-axis or reflection in \(y = 0\) | B1 |
Additional guidance
| Reflect(ed) in the \(x\)-axis | B1 |
| Do not allow if there is additional incorrect information eg1 Reflection in the \(x\)-axis about the origin eg2 Reflection in the \(x\)-axis and rotated | B0 B0 |
| Reflection | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Rotation through 180° centre the origin or enlargement scale factor \(-1\) centre the origin | B2 | B1 \(\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}\) or enlargement scale factor \(-1\) or rotation through 180° or indication that B represents rotation through 270° (anticlockwise centre the origin) or indication that B represents rotation through 90° clockwise (centre the origin) |
Additional guidance
| For B2 ignore any reference to clockwise or anticlockwise rotation | |
| Condone omission of degrees symbol throughout eg B is rotation through 270 | B1 |
| Mark intention eg1 Rotate(d) 180 about \(O\) eg2 Enlarge(d) sf \(-1\) | B2 B1 |
| Allow rotation through 540 centre the origin | B2 |
| Do not allow if there is additional information that is incorrect eg1 Rotation through 180° and a reflection eg2 Enlargement sf \(-1\) rotated through 90° eg3 Rotation through 180° centre the origin so the shape turns | B0 B0 B2 |
| Rotation | B0 |
| Enlargement | B0 |
| Do not allow turn for rotation | |
| Do not allow eg half turn for 180° | |
| Do not allow negative enlargement |