Transformations (AQA GCSE Maths: Higher): Exam Questions

Rotate triangle A $90°$ clockwise, centre $O$.

Enlarge triangle B by scale factor 3, centre (1, 2).

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

Reflect shape P in the line $x=-1$. 

Rotate shape P $90°$ anticlockwise about (0, 1).

Rotate triangle A $90°$ anticlockwise with centre $O$.

Describe fully the single transformation that maps triangle B onto triangle C.

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

Translate shape A by the vector $\left(\begin{array}{c}-3\\ 2\end{array}\right).$

Describe fully the single transformation that maps shape Q onto shape R.

Translate shape P by the vector $\left(\begin{array}{c}5\\ -2\end{array}\right)$.

Describe fully the single transformation that maps shape A onto shape B.

On the grid, rotate shape S by $90°$ anticlockwise about the origin.

Describe fully the single transformation that maps shape P onto shape Q.

On the grid, rotate shape A $180°$ about the point (1, 1).

On the grid, enlarge triangle B by scale factor 3, centre (0, 0).

Describe fully the single transformation that maps shape P onto shape Q.

Triangles J and L are drawn on the grid below.

What is the scale factor of the enlargement that maps triangle L onto triangle J?

Shape A can be transformed to shape B by a reflection in the x-axis followed by a translation $\left(\begin{array}{c}c\\ d\end{array}\right)$
Find the value of c and the value of $d$.

$OABC$ is enlarged, scale factor 2, centre (0, 0)

Circle the number of invariant points on the perimeter of the square.

$OABC$ is reflected in the line $y=x$
Circle the number of invariant points on the perimeter of the square.

$ABCD$ is a quadrilateral.

The quadrilateral is reflected in the line $x=4$

Which vertices are invariant?

Circle your answer.

Shape A and shape C are shown on the grid below.

Reflect shape A in the line $x=2$

Label the image B.

Describe fully the single transformation that maps shape B onto shape C.

Enlarge shape A by scale factor  $\frac{1}{3}$ centre (0, 1).

The diagram shows triangle A drawn on a grid.

Kyle reflects triangle A in the $x$-axis to get triangle B.
He then reflects triangle B in the line $y=x$ to get triangle C.

Amy reflects triangle A in the line $y=x$ to get triangle D.
She is then going to reflect triangle D in the $x$-axis to get triangle E.

Amy says that triangle E should be in the same position as triangle C.

Is Amy correct?
You must show how you get your answer.

Shape P is reflected in the line $x=-1$ to give shape Q.

Shape Q is reflected in the line $y=0$ to give shape R.

Describe fully the single transformation that maps shape P onto shape R.

Shape T is reflected in the line $x=-1$ to give shape R.
Shape R is reflected in the line $y=-2$ to give shape S.

Describe the single transformation that will map shape T to shape S.

Triangle $ABC$ is drawn on a centimetre grid.
$A$ is the point (2, 2).
$B$ is the point (6, 2).
$C$ is the point (5, 5).

Triangle $PQR$ is an enlargement of triangle $ABC$ with scale factor $\frac{1}{2}$ and centre (0, 0).
Work out the area of triangle $PQR$.

Enlarge the shaded triangle by a scale factor $1\frac{1}{2}$, centre $P$.

Enlarge triangle T, scale factor $-2$, centre $O$.

Enlarge shape J using scale factor ^-2 and centre (0, 2). Label your image K.

Shape S is shown on the grid.

Enlarge shape S with scale factor −2 and centre (0, 0).
Label your image E.

On the grid, draw the image of shape A after an enlargement with scale factor −2, centre (0, 1),

Draw the enlargement of shape Q, centre (0, 0), scale factor -2.

On the grid above, draw the enlargement of triangle A by scale factor -4, with centre (0, 1).
Label the image E.

Describe fully the enlargement that maps triangle T onto triangle U.

ABC is a right-angled triangle.

Here is Sarah's method to find the length of $BC$.

$\begin{array}{rcl}B{C}^2& =& A{B}^2+A{C}^2\\ & =& 6^2+8^2\\ & =& 100\\ BC& =& 10\end{array}$

What mistake has Sarah made in her method?

Roy is going to enlarge triangle $PQR$ with centre $C$ and scale factor $1\frac{1}{2}$

He draws triangle $XYZ$.

Explain why Roy's diagram is not correct.

Triangle $PQR$ is shown.

When $PQR$is reflected in a line,$P$and $R$ are invariant points.

Circle the equation of the line.

A sketch of a quadrilateral $PQRS$ is shown.

$PQRS$ is reflected in the line $y=x$

Circle the vertex that is invariant.

Here is a shape $\mathbf{P}$drawn on a grid of squares.

On the grid, rotate shape $\mathbf{P}$ 180° about the point (–3, 2)
Label the new shape $\mathbf{Q}$.

Describe fully the single transformation that maps triangle $\mathbf{A}$ onto triangle $\mathbf{B}.$

Triangle A is rotated $90°$ clockwise about the point (0, 1) to give triangle B.

Triangle B is translated by the vector $\left(\begin{array}{c}-3\\ -1\end{array}\right)$ to give triangle C.

Describe fully the single transformation that maps triangle A onto triangle C.

Enlarge shape A by scale factor −2, centre (0, 0)
Label your image B.

Describe fully the single transformation that will map shape B onto shape A.

The triangle $ABC$ is to be enlarged, using $E$ as the centre, to give the triangle $PQR$.
The line $PQ$ is the image of the line $BA$.

Write down the scale factor of the enlargement.

The triangle $ABC$ is to be enlarged, using $E$ as the centre, to give the triangle $PQR$.
The line $PQ$ is the image of the line $BA$.

Complete the triangle $PQR$.

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

Enlarge the shaded shape by scale factor $-\frac{1}{2}$ with centre (−1, −2).

On the grid, enlarge the triangle by scale factor $-\frac{1}{2}$, centre (0, −2).

Enlarge shape P by scale factor $-\frac{1}{2}$ with centre of enlargement (0, 0).
Label your image Q.

On the grid, enlarge the triangle by scale factor $-1\frac{1}{2}$ , centre (0, 2).

Enlarge triangle A by scale factor $-1\frac{1}{2}$, centre $O$.

Enlarge triangle A by scale factor $-\frac{1}{2}$, centre (−1, −2).
Label your triangle B.

Enlarge shape T with scale factor −1.5, centre (0, 2).

Enlarge the triangle by a scale factor of $-\frac{1}{2}$, centre $O$.