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

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

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.

Problem solving with further transformations

Maths

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.

Further transformations

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

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

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 $$\begin{pmatrix} 3 \\ -2 \\ \end{pmatrix}$$

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?

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

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 rotation of 90° clockwise about the origin

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

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 $$\begin{pmatrix} -6 \\ 0 \\ \end{pmatrix}$$ 

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?

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

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

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

Select the transformations that map shape A onto shape B.

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

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

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

Describe the transformation that maps shape A onto shape H. 

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

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

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

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