Identifying multiple transformations | Maths | Quizalize & Oak National Academy

Starter quiz

A vector can be used to describe a __________.

enlargement

reflection

rotation

translation ✓
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''.

P'(2, 2)

P'(6, 6) ✓

P''(6, 2) ✓

P''(6, 6)

P''(2, 2)
$Sofia translates shape A by <Math>\begin{pmatrix} 1 \\ -3 \\ \end{pmatrix}</Math> to A'. She then reflects A' in the line <Math>x=5</Math> to A''. Select the coordinates of P' and P''.$

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''.

P'(4, 3)

P'(3, 3) ✓

P''(5, 3)

P''(6, 3)

P''(7, 3) ✓
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°

-45° ✓

45°

315° ✓
Here are some buttons that you can use in Desmos for transformations. Match each button to its function.

Button a

⇔

reflects object ✓

Button b

⇔

selects object ✓

Button c

⇔

rotates object ✓

Button d

⇔

translates object ✓
Match each transformation to its description.

Shape E to shape D

⇔

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

Shape D to shape C

⇔

Reflection in the line $x=4$ ✓

Shape C to shape B

⇔

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

Shape B to shape A

⇔

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

Exit quiz

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

centre

constant

invariant ✓

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

angle ✓

centre ✓

direction ✓

scale factor

vector
What type of transformation maps shape A onto shape B?

A translation

A rotation ✓

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

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 $(3, 2)$
Describe the transformation that maps shape A onto shape E.

a reflection

a translation ✓

in the line $y=x$

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

by the vector $\begin{pmatrix} 8 \\ 5 \\ \end{pmatrix}$
Select the two transformations needed to map shape A onto shape C.

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 $(3, 3)$

Worksheet

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Video

Lesson Details

Key learning points

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

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.

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.