A transformation is a process that may change the size, orientation or position of a shape.

A reflection of a shape is the mirror image of the shape. An object is reflected when it is flipped over a fixed line (line of reflection), without the image being turned or its size changing.

The line of reflection is the fixed line about which an object is reflected. The object and image are equidistant from the line of reflection.

The object is the starting figure, before a transformation has been applied.

The image is the resulting figure, after a transformation has been applied.

Checking and securing understanding of reflection

Maths

Checking and securing understanding of congruence and similarity

Checking and securing understanding of rotation

Checking and securing understanding of translation

Checking and securing understanding of enlargement with positive integer scale factors

Checking and securing understanding of enlargement with positive fractional scale factors

Multiple transformations

Identifying multiple transformations

Problem solving with further transformations

In this unit, pupils enhanced their understanding of enlargement. In this future unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape. 

In the prior unit, pupils learnt about the different types of transformations. In this unit, pupils' knowledge is extended as negative scale factors are considered as are multiple transformations.

In this unit pupils apply their knowledge of transformations to explore negative enlargement factors and the application of multiple transformations.

Further transformations

A reflection of a shape is the {{ }} image of the shape.

Which of these diagrams show a reflection?

Shape A is reflected onto shape B. What is the equation of the line of reflection?

A translation by the vector $$\begin{pmatrix} 3 \\ -3 \\ \end{pmatrix}$$

A rotation of 180° clockwise about the origin

The point $$P$$ has coordinates $$(3, -2)$$. $$P$$ is reflected in different lines of reflection. Match the coordinates of the image of $$P$$ to the equation of the line of reflection.

A translation is a {{}} in which every point of a shape moves the same distance in the same direction.

$$\begin{pmatrix} -4 \\ -5 \\ \end{pmatrix}$$

$$\begin{pmatrix} 4 \\ 5 \\ \end{pmatrix}$$

$$\begin{pmatrix} -5 \\ 4 \\ \end{pmatrix}$$

$$\begin{pmatrix} 5 \\ -4 \\ \end{pmatrix}$$

$$\begin{pmatrix} -4 \\ 5 \\ \end{pmatrix}$$

$$\begin{pmatrix} 5 \\ 4 \\ \end{pmatrix}$$

Match each description to the correct vector.

The point P(4, 3) is translated by the vector $$\begin{pmatrix} -2 \\ 1 \\ \end{pmatrix}$$ to P'. What are the coordinates of P'?

Translation by  $$\begin{pmatrix} -3 \\ 2 \\ \end{pmatrix}$$

Translation by  $$\begin{pmatrix} 3 \\ -2 \\ \end{pmatrix}$$

$$\begin{pmatrix} 2 \\ 3 \\ \end{pmatrix}$$

$$\begin{pmatrix} -2 \\ 3 \\ \end{pmatrix}$$

$$\begin{pmatrix} 2 \\ -3 \\ \end{pmatrix}$$

Shape P is translated onto shape Q by the vector $$\begin{pmatrix} -3 \\ 2\\ \end{pmatrix}$$. What transformation will map shape Q onto shape P?

B is translated by  $$\begin{pmatrix} 0 \\ 2 \\ \end{pmatrix}$$ onto C

C is translated by  $$\begin{pmatrix} 1 \\ -2 \\ \end{pmatrix}$$ onto D

D is translated by  $$\begin{pmatrix} 1 \\ 3 \\ \end{pmatrix}$$ onto E

E is translated by  $$\begin{pmatrix} -1 \\ -1\\ \end{pmatrix}$$ onto F

F is translated by  $$\begin{pmatrix} -7 \\ -2\\ \end{pmatrix}$$ onto A

Checking and securing understanding of reflection

Lesson outcome