Higher June 2019 Paper 3 Q25
25 \(ABCD\) is a square.
\(A\) is \((-2, 1) \quad B\) is \((0, -1) \quad C\) is \((2, 1) \quad D\) is \((0, 3)\)
(a) A single transformation of \(ABCD\) is such that
\(B\) is mapped to \(D\)
\(D\) is mapped to \(B\)
\(A\) and \(C\) are invariant points.
Describe fully the transformation. [2 marks]
(b) A different single transformation of \(ABCD\) is such that
\(B\) is mapped to \(D\)
\(D\) is mapped to \(B\)
the only invariant point is (0, 1)
Describe fully the transformation. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Reflection | B1 | |
| \(y = 1\) or \(AC\) | B1 |
Additional guidance
| Mirror line | B0 |
| Contradiction for line of reflection | B0 |
| More than one transformation given | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Rotation | B1 | |
| Centre (0, 1) | B1 | |
| 180° | B1 | degrees symbol does not have to be seen |
| Alternative method 2 | ||
| Enlargement | B1 | |
| Centre (0, 1) | B1 | |
| Scale factor \(-1\) | B1 | |
Additional guidance
| For centre (0, 1) allow about (0, 1) or (0, 1) | B1 |
| For centre (0, 1) do not allow 0, 1 | B0 |
| More than one transformation given eg rotation then translation | B0 |
| Do not allow half turn for 180° | |
| Ignore clockwise or anticlockwise | |
| For scale factor allow sf or scale or (\(\times\)) \(-1\) |