The diagram shows two shapes, A and B, on a grid.
(a) Describe fully the single transformation that maps shape A onto shape B.
(b) On the grid, draw the image of shape A after a reflection in the line $x =-1$.
▶️ Answer/Explanation
(a) Ans: Rotation, 90° anticlockwise about (0,0)
Observe the positions of shapes A and B. Shape A is rotated 90° anticlockwise around the origin (0,0) to align perfectly with shape B. The transformation preserves the shape’s size and orientation relative to the rotation.
(b)
To reflect shape A over the line $x = -1$, each point of A is mirrored across the vertical line at $x = -1$. The reflected image will be congruent but flipped, maintaining the same distance from the line of reflection.
$\textbf{v}= \begin{pmatrix} -1\\ 3\end{pmatrix}$, $\textbf{y}= \begin{pmatrix} 2\\ 5\end{pmatrix}$
Find:
$(a)\; \textbf{v} – \textbf{y}$
$(b)\; 2\textbf{v}$
▶️ Answer/Explanation
Ans:
(a) \( \begin{pmatrix} -3 \\ -2 \end{pmatrix} \)
(b) \( \begin{pmatrix} -2 \\ 6 \end{pmatrix} \)
Explanation:
(a) Subtract corresponding components of vectors \(\textbf{v}\) and \(\textbf{y}\):
\[ \textbf{v} – \textbf{y} = \begin{pmatrix} -1 – 2 \\ 3 – 5 \end{pmatrix} = \begin{pmatrix} -3 \\ -2 \end{pmatrix} \]
(b) Multiply each component of \(\textbf{v}\) by 2:
\[ 2\textbf{v} = \begin{pmatrix} -2 \\ 6 \end{pmatrix} \]