By understanding what changes and what is invariant, you can determine whether a transformation has occurred.
Sometimes you might need to persevere in order to find the right transformation(s).
You may be able to check your deductions by carrying out the transformation.

Common misconception

There is only one way to describe what has happened to an object to create its image.

There may be multiple transformations or combinations of transformations that map the object to the image.

Keywords

Object - The object is the starting figure, before a transformation has been applied.
Image - The image is the resulting figure, after a transformation has been applied.
Sense - The sense of an object is the direction of the orientation of the object. When the sense of an object changes, the direction of its orientation changes from clockwise to anti-clockwise, or vice versa.

Pupils may benefit from having access to tracing paper so that they can investigate different types of transformation. Encourage them to find the smallest number of transformations and state what they are. Which transformations are not helpful for each case and why?

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

A point on a shape is invariant if that point has __________ location after the shape is transformed.

changed

Correct answer: not changed

reflected

rotated

translated

Q2.

Select the information you should give to fully describe an enlargement.

angle

Correct answer: centre

direction

Correct answer: scale factor

vector

Q3.

Select the transformations that map shape A onto shape B.

A reflection in the line $$x=0$$

Correct answer: A reflection in the line $$y=0$$

Correct answer: A rotation of 180° about (3, 0)

A rotation of 90° about (0 0)

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

Q4.

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

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

A reflection in the line $$x=3$$

Correct answer: A rotation of $$180$$° about $$(3, 2)$$

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

Q5.

Describe the transformation that maps shape A onto shape H.

Correct answer: An enlargement

Correct answer: centre $$(-6, 5)$$

centre $$(-5, 4)$$

Correct answer: scale factor $$2$$

scale factor $$\frac{1}{2}$$

Q6.

Select the two transformations needed to map shape B onto shape D.

Correct answer: A reflection in the line $$y=x$$

A rotation of $$90$$° about $$(3, 3)$$

followed by a reflection in the line $$y=5$$

Correct answer: followed by a reflection in the line $$x=5$$

Exit quiz

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6 Questions

Q1.

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

Correct Answer: object

Q2.

Shape A is mapped onto shape B by a rotation of ° clockwise about (3, 2).

Correct Answer: 180

Q3.

Jun translates an object by the vector $$\begin{pmatrix} 2 \\ -3 \\ \end{pmatrix}$$ onto its image. What transformation will map the image back onto the object?

A translation by $$\begin{pmatrix} -2 \\ -3 \\ \end{pmatrix}$$

A translation by $$\begin{pmatrix} -3 \\ 2 \\ \end{pmatrix}$$

Correct answer: A translation by $$\begin{pmatrix} -2 \\ 3 \\ \end{pmatrix}$$

A translation by $$\begin{pmatrix} 2 \\ 3 \\ \end{pmatrix}$$

A translation by $$\begin{pmatrix} 3 \\ -2 \\ \end{pmatrix}$$

Q4.

Laura reflects an object in the line $$x=-2$$ onto its image. What transformation will map the image back onto the object?

Reflection in the line $$x=2$$

Correct answer: Reflection in the line $$x=-2$$

Reflection in the line $$y=-2$$

Reflection in the line $$y=2$$

Q5.

Select the two transformations needed to map shape D onto shape B.

Correct answer: First a translation by the vector $$\begin{pmatrix} -2 \\ -2 \\ \end{pmatrix}$$

First a translation by the vector $$\begin{pmatrix} -2 \\ -4\\ \end{pmatrix}$$

Then a reflection in the line $$y=x$$

Correct answer: Then a rotation of 90° clockwise about the origin

Q6.

Shape C is translated by $$\begin{pmatrix} -3 \\ 0 \\ \end{pmatrix}$$ and then its image is enlarged by s.f. 2 about (8, -2). What single transformation is equivalent will have the same result?

An enlargement scale factor 2 about (7, 3)

An enlargement scale factor 2 about (5, 2)

Correct answer: An enlargement scale factor 2 about (8, 4)

A translation by $$\begin{pmatrix} 3 \\ 0 \\ \end{pmatrix}$$

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