Transformations of Shapes: Eduqas GCSE Foundation November 2021 Paper 2 Q22

Foundation November 2021 Paper 2 Q22

EduqasFoundationCurrent spec6 marksTransformations of Shapes Vectors

22.

(a)

Diagram: coordinate grid from -6 to 6 on both axes, with L-shaped shape A with vertices (-4, 2), (-4, 5), (-3, 5), (-3, 3), (-2, 3), (-2, 2)

\(\mathbf{p}\) 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]

You may use this grid to help you.

Diagram: coordinate grid with x from -2 to 10 and y from -2 to 10, showing triangle C with vertices (4, 3), (6, 5), (6, 0)

Transformation: ………………

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 \(y \neq -1\) or \(\begin{pmatrix}x\\-1\end{pmatrix}\) where \(x \neq 6\) 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.
	(6)