(a)\(\mathbf{p}\) and \(\mathbf{q}\) are translation vectors with\[\mathbf{p} = \begin{pmatrix} 3 \\ -5 \end{pmatrix} \quad\text{and}\quad \mathbf{q} = \begin{pmatrix} 1{\cdot}5 \\ 2 \end{pmatrix}.\]Shape \(A\) is mapped to shape \(B\) using \(\mathbf{p} + 2\mathbf{q}\).
(i) Find the column vector which translates shape \(A\) to shape \(B\). [2]
(ii) Draw and label shape \(B\) on the grid. [2]
(b) Triangle \(C\) has vertices with coordinates (4, 3), (6, 5), (6, 0). After a single transformation, the vertices of triangle \(C\) are mapped to (3, 4), (5, 6), (0, 6).
Describe the transformation. [2]
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Mark scheme (a)
Scheme
Marks
Comments
(i) \(\begin{pmatrix} 6 \\ -1 \end{pmatrix}\)
B2
B1 for sight of \(\begin{pmatrix} 3 \\ -5 \end{pmatrix} + \begin{pmatrix} 3 \\ 4 \end{pmatrix}\) Allow B1 for \(\begin{pmatrix} 6 \\ -1 \end{pmatrix}\) written incorrectly e.g. \(\left(\dfrac{6}{-1}\right)\)
(ii) Correct shape \(B\) drawn at (2, 1), (2, 4), (3, 4), (3, 2), (4, 2), (4, 1),
B2
or correct FT; FT ‘their \(\begin{pmatrix} 6 \\ -1 \end{pmatrix}\)’
B1 for a translation attempted with at least 4 vertices correct or shape \(A\) correctly translated by \(\begin{pmatrix} 6 \\ y \end{pmatrix}\) where \(y \ne -1\) or \(\begin{pmatrix} x \\ -1 \end{pmatrix}\) where \(x \ne 6\)
If no marks in (a) then award SC1 for a clear attempt to translate by \(\begin{pmatrix} 3 \\ -5 \end{pmatrix}\) and \(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\).
Mark scheme (b)
Scheme
Marks
Comments
Reflection (in the line) \(y = x\)
B2
B1 for either stating a reflection or giving the equation \(y = x\)
Award no marks if more than one transformation indicated
If no marks then award SC1 for a correct diagram with the line \(y = x\) drawn.
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