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

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

A vector can be used to describe a translation.

A property of a shape is invariant if that property has not changed after the shape is transformed.

Identifying multiple transformations

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 reflection

Checking and securing understanding of enlargement with positive integer scale factors

Checking and securing understanding of enlargement with positive fractional scale factors

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 point on a shape is __________ if that point has not changed location after the shape is transformed.

Select the information you should give to fully describe a rotation. 

What type of transformation maps shape A onto shape B?

A translation by the vector $$\begin{pmatrix} 2 \\ 0 \\ \end{pmatrix}$$

An enlargement scale factor -1 about $$(3, 2)$$

Describe one possible transformation from A to B that has zero invariant points.

by the vector $$\begin{pmatrix} 8 \\ -5 \\ \end{pmatrix}$$

by the vector $$\begin{pmatrix} 8 \\ 5 \\ \end{pmatrix}$$

Describe the transformation that maps shape A onto shape E.

A translation by the vector  $$\begin{pmatrix} 6 \\ 0 \\ \end{pmatrix}$$

A translation by the vector  $$\begin{pmatrix} 0 \\ 6 \\ \end{pmatrix}$$

followed by a reflection in the line $$y=x$$

followed by a rotation of $$90$$° about $$(3, 3)$$

Select the two transformations needed to map shape A onto shape C.

A vector can be used to describe a __________.

Andeep reflects shape A in the line $$x=4$$ to A'. He then reflects A' in the line $$y=4$$ to A''. Select the coordinates of P' and P''.

Sofia translates shape A by  $$\begin{pmatrix} 1 \\ -3 \\ \end{pmatrix}$$ to A'. She then reflects A' in the line $$x=5$$ to A''. Select the coordinates of P' and P''.

Laura is using technology to transform some shapes. She wants to use Desmos to rotate a shape 45° clockwise. Which of these angles should Laura type into Desmos?

Here are some buttons that you can use in Desmos for transformations. Match each button to its function.

Enlargement, scale factor $$\frac{1}{2}$$, about $$(6,-3)$$

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

Rotation $$90$$° anticlockwise about $$(4, 1)$$

Match each transformation to its description.

Starter Quiz

A vector can be used to describe a __________.