Transformations: rotation, reflection, translation & enlargement

Shape A is drawn on the grid.

(a) On the grid, translate shape A by the vector $\begin{pmatrix} -5 \\ 2 \end{pmatrix}$. Label the new shape B. [2]

(b) The point $(2,\ 5)$ is translated by the vector $\begin{pmatrix} 3 \\ -4 \end{pmatrix}$.
Write down the coordinates of its image. [1]

Shape Q and the line L are drawn on the grid.

(a) Write down the equation of the line L. [1]

(b) On the grid, reflect shape Q in the line L. [2]

Shape R is drawn on the grid.

On the grid, rotate shape R $90^\circ$ clockwise about the point $(1,\ 0)$. [2]

Triangle A and triangle B are drawn on the grid.

Describe fully the single transformation that maps triangle A onto triangle B. [3]

Triangles P, Q and R are drawn on the grid.

(a) Describe fully the single transformation that maps triangle P onto triangle Q. [2]

(b) Describe fully the single transformation that maps triangle P onto triangle R. [2]

Shape S and the point C are drawn on the grid.

On the grid, enlarge shape S by scale factor $\tfrac{1}{2}$ with centre C. [2]

Triangle A and triangle B are drawn on the grid.

Describe fully the single transformation that maps triangle A onto triangle B. [3]

Triangle $ABC$ has $AB = 8\text{ cm}$ and angle $ABC = 35^\circ$.

(a) Triangle $ABC$ is rotated $90^\circ$ clockwise about a point to give triangle $PQR$, where $A$ maps to $P$, $B$ maps to $Q$ and $C$ maps to $R$.
Write down the length of $PQ$ and the size of angle $PQR$. [1]

(b) Triangle $ABC$ is enlarged by scale factor $1.5$ to give triangle $DEF$, where $A$ maps to $D$, $B$ maps to $E$ and $C$ maps to $F$.
(i) Work out the length of $DE$. [1]
(ii) Write down the size of angle $DEF$. [1]

(c) Hana says,
“Triangle $DEF$ is congruent to triangle $ABC$ because all the angles are the same.”
Is Hana correct? Give a reason for your answer. [1]

(d) Triangle $ABC$ is enlarged by scale factor $0.4$ to give triangle $GHI$, where $A$ maps to $G$ and $B$ maps to $H$.
Work out the length of $GH$. [1]

Triangle T is drawn on the grid.

(a) On the grid, reflect triangle T in the line $y = x$. Label the image A. [2]

(b) On the grid, rotate triangle A $90^\circ$ anticlockwise about the origin $O$. Label the image B. [1]

(c) Describe fully the single transformation that maps triangle T onto triangle B. [2]

The point $P$ has coordinates $(1,\ 6)$.

(a) $P$ is reflected in the straight line $L$. The image of $P$ is the point $(5,\ 2)$.
Find an equation of the line $L$. [3]

(b) $P$ is rotated $90^\circ$ clockwise about the point $C$. The image of $P$ is the point $(7,\ 2)$.
Find the coordinates of $C$.
Show your working clearly. [3]