Problem solving with further transformations | Maths | Quizalize & Oak National Academy

Starter quiz

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

changed

not changed ✓

reflected

rotated

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

angle

centre ✓

direction

scale factor ✓

vector
Select the transformations that map shape A onto shape B.

A reflection in the line $x=0$

A reflection in the line $y=0$ ✓

A rotation of 180° about (3, 0) ✓

A rotation of 90° about (0 0)

A translation by $\begin{pmatrix} 0 \\ -6 \\ \end{pmatrix}$
Describe one possible transformation from A to B that has one invariant point.

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

A reflection in the line $x=3$

A rotation of $180$ ° about $(3, 2)$ ✓

A translation by the vector $\begin{pmatrix} 2 \\ 0 \\ \end{pmatrix}$
Describe the transformation that maps shape A onto shape H.

An enlargement ✓

centre $(-6, 5)$ ✓

centre $(-5, 4)$

scale factor $2$ ✓

scale factor $\frac{1}{2}$
Select the two transformations needed to map shape B onto shape D.

A reflection in the line $y=x$ ✓

A rotation of $90$ ° about $(3, 3)$

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

followed by a reflection in the line $x=5$ ✓

Exit quiz

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

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

'180' ✓
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 $\begin{pmatrix} -3 \\ 2 \\ \end{pmatrix}$

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

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

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

Reflection in the line $x=-2$ ✓

Reflection in the line $y=-2$

Reflection in the line $y=2$
Select the two transformations needed to map shape D onto shape B.

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 $y=x$

Then a rotation of 90° clockwise about the origin ✓
$Shape C is translated by <Math>\begin{pmatrix} -3 \\ 0 \\ \end{pmatrix}</Math> and then its image is enlarged by s.f. 2 about (8, -2). What single transformation is equivalent will have the same result?$

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)

An enlargement scale factor 2 about (8, 4) ✓

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

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

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Lesson Details

Key learning points

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.