New
New
Year 10
Higher

Identifying multiple transformations

I can identify what transformations have taken place.

New
New
Year 10
Higher

Identifying multiple transformations

I can identify what transformations have taken place.

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Lesson details

Key learning points

  1. More than one transformation may have taken place.
  2. If the size has changed, one shape may be an enlargement of the other.
  3. If the orientation has changed, one shape may be a rotation of the other.
  4. If the shapes are mirrored, one shape may be a reflection of the other.
  5. If the shapes look identical but are in different places, one may be a translation of the other.

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.

  • Vector - A vector can be used to describe a translation.

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

Common misconception

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

Learning cycle 1 explores how different transformations can produce the same image. This is a good way of demonstrating that there is more than one possible description.

Some pupils may benefit from having the slides printed out so that they can check the transformations using tracing paper.
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).

Lesson video

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6 Questions

Q1.
A vector can be used to describe a __________.
enlargement
reflection
rotation
Correct answer: translation
Q2.
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''.
An image in a quiz
P'(2, 2)
Correct answer: P'(6, 6)
Correct answer: P''(6, 2)
P''(6, 6)
P''(2, 2)
Q3.
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''.
An image in a quiz
P'(4, 3)
Correct answer: P'(3, 3)
P''(5, 3)
P''(6, 3)
Correct answer: P''(7, 3)
Q4.
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?
-315°
Correct answer: -45°
45°
Correct answer: 315°
Q5.
Here are some buttons that you can use in Desmos for transformations. Match each button to its function.
An image in a quiz
Correct Answer:Button a,reflects object

reflects object

Correct Answer:Button b,selects object

selects object

Correct Answer:Button c,rotates object

rotates object

Correct Answer:Button d,translates object

translates object

Q6.
Match each transformation to its description.
An image in a quiz
Correct Answer:Shape E to shape D,Enlargement, scale factor $$\frac{1}{2}$$, about $$(6,-3)$$

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

Correct Answer:Shape D to shape C,Reflection in the line $$x=4$$

Reflection in the line $$x=4$$

Correct Answer:Shape C to shape B,Translation by $$\begin{pmatrix} 4 \\ 5 \\ \end{pmatrix}$$

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

Correct Answer:Shape B to shape A,Rotation $$90$$° anticlockwise about $$(4, 1)$$

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

6 Questions

Q1.
A point on a shape is __________ if that point has not changed location after the shape is transformed.
centre
constant
Correct answer: invariant
variable
Q2.
Select the information you should give to fully describe a rotation.
Correct answer: angle
Correct answer: centre
Correct answer: direction
scale factor
vector
Q3.
What type of transformation maps shape A onto shape B?
An image in a quiz
A translation
Correct answer: A rotation
Correct answer: A reflection
Q4.
Describe one possible transformation from A to B that has zero invariant points.
An image in a quiz
Correct answer: A translation by the vector $$\begin{pmatrix} 2 \\ 0 \\ \end{pmatrix}$$
A rotation of $$180$$° about $$(3, 2)$$
A reflection in the line $$x=3$$
An enlargement scale factor -1 about $$(3, 2)$$
Q5.
Describe the transformation that maps shape A onto shape E.
An image in a quiz
a reflection
Correct answer: a translation
in the line $$y=x$$
Correct answer: by the vector $$\begin{pmatrix} 8 \\ -5 \\ \end{pmatrix}$$
by the vector $$\begin{pmatrix} 8 \\ 5 \\ \end{pmatrix}$$
Q6.
Select the two transformations needed to map shape A onto shape C.
An image in a quiz
Correct answer: A translation by the vector $$\begin{pmatrix} 6 \\ 0 \\ \end{pmatrix}$$
A translation by the vector $$\begin{pmatrix} 0 \\ 6 \\ \end{pmatrix}$$
Correct answer: followed by a reflection in the line $$y=x$$
followed by a rotation of $$90$$° about $$(3, 3)$$