New
New
Year 10
•
Higher
Advanced problem solving with further transformations
I can use my enhanced knowledge of transformations to solve problems.
New
New
Year 10
•
Higher
Advanced problem solving with further transformations
I can use my enhanced knowledge of transformations to solve problems.
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.
Invariant - A property of a shape is invariant if that property has not changed after the shape is transformed.
Invariant point - A point on a shape is invariant if that point has not changed location after the shape is transformed.
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).
Video
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Starter quiz
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6 Questions
Q1.
A point on a shape is if that point has not changed location after the shape is transformed.
Correct Answer: invariant
invariant
Q2.
Select the statements which fully describe a transformation.
enlargement by scale factor 3
Correct answer: reflection in the $$y$$-axis
reflection in the $$y$$-axis
rotation of 90° about the origin
Q3.
What type of transformation maps shape B onto shape A?
A reflection in the line $$x=0$$
Correct answer: A reflection in the line $$y=0$$
A reflection in the line $$y=0$$
Correct answer: A rotation of 180° about (3, 0)
A rotation of 180° about (3, 0)
A rotation of 90° about (0 0)
Correct answer: An enlargement scale factor -1 about (3, 0)
An enlargement scale factor -1 about (3, 0)
Q4.
Describe one possible transformation from A to B that has a collection of invariant points.
An enlargement scale factor -1 about $$(3, 2)$$
Correct answer: A reflection in the line $$x=3$$
A reflection in the line $$x=3$$
A rotation of $$180$$° about $$(3, 2)$$
A translation by the vector $$\begin{pmatrix} 2 \\ 0 \\ \end{pmatrix}$$
Q5.
Select the two transformations needed to map shape H onto shape E.
An enlargement scale factor $$\frac{1}{2}$$ about centre $$(-5, 4)$$
Correct answer: An enlargement scale factor $$\frac{1}{2}$$ about centre $$(-6, 5)$$
An enlargement scale factor $$\frac{1}{2}$$ about centre $$(-6, 5)$$
Correct answer: followed by a translation by $$\begin{pmatrix} 8 \\ -5 \\ \end{pmatrix}$$
followed by a translation by $$\begin{pmatrix} 8 \\ -5 \\ \end{pmatrix}$$
followed by a translation by $$\begin{pmatrix} 8 \\ 5 \\ \end{pmatrix}$$
Q6.
Select the two transformations needed to map shape B onto shape G.
Correct answer: A reflection in the line $$y$$ = 0
A reflection in the line $$y$$ = 0
A reflection in the line $$x$$ = 0
followed by a reflection in the line $$y=x$$
Correct answer: followed by a rotation of 90° clockwise about the origin
followed by a rotation of 90° clockwise about the origin
followed by a rotation of 90° clockwise about the (0, -1)
Exit quiz
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6 Questions
Q1.
The object is the starting figure, before a transformation has been applied. The is the resulting figure, after a transformation has been applied.
Correct Answer: image
image
Q2.
Shape A is mapped onto shape B by a reflection. The equation of line that contains the invariant points is .
Correct Answer: x=3, x = 3, x= 3, x =3
x=3, x = 3, x= 3, x =3
Q3.
Sofia transforms an object by the vector $$\begin{pmatrix} -4 \\ 3 \\ \end{pmatrix}$$ onto its image. What transformation will map the image back onto the object?
A translation by $$\begin{pmatrix} -4 \\ -3 \\ \end{pmatrix}$$
Correct answer: A translation by $$\begin{pmatrix} 4 \\ -3 \\ \end{pmatrix}$$
A translation by $$\begin{pmatrix} 4 \\ -3 \\ \end{pmatrix}$$
A translation by $$\begin{pmatrix} -3 \\ 4 \\ \end{pmatrix}$$
A translation by $$\begin{pmatrix} 4 \\ 3 \\ \end{pmatrix}$$
A translation by $$\begin{pmatrix} 3 \\ -4 \\ \end{pmatrix}$$
Q4.
Jacob enlarges an object by a scale factor of $$-2$$ about $$(2, -3)$$. What transformation will map the image back onto the object?
Enlargement scale factor $$2$$ about $$(-2, 3)$$
Enlargement scale factor $$\frac{1}{2}$$ about $$(2, 3)$$
Enlargement scale factor $$-\frac{1}{2}$$ about $$(-2, 3)$$
Enlargement scale factor $$-2$$ about $$(2, -3)$$
Correct answer: Enlargement scale factor $$-\frac{1}{2}$$ about $$(2, -3)$$
Enlargement scale factor $$-\frac{1}{2}$$ about $$(2, -3)$$
Q5.
Some Oak pupils are discussing invariant points after a transformation. Which pupils are correct?
Correct answer: Jun: A rotation carried out about any point P on an object has P as invariant
Jun: A rotation carried out about any point P on an object has P as invariant
Sam: A rotation of a triangle can give a single line of invariant points
Correct answer: Andeep: A translation never gives an invariant point unless the vector is 0
Andeep: A translation never gives an invariant point unless the vector is 0
Correct answer: Aisha: A reflection about a line on the shape gives a line of invarient points
Aisha: A reflection about a line on the shape gives a line of invarient points
Jacob: An enlargement about a point not on the object gives one invariant point
Q6.
Shape I is enlarged by s.f. $$\frac{1}{2}$$ about (8, -2) and its image is translated $$\begin{pmatrix} 3 \\ 0 \\ \end{pmatrix}$$. What single transformation is equivalent will have the same result?
An enlargement scale factor $$-\frac{1}{2}$$ about (5, 2)
Correct answer: An enlargement scale factor $$\frac{1}{2}$$ about (8, 4)
An enlargement scale factor $$\frac{1}{2}$$ about (8, 4)
An enlargement scale factor $$-\frac{1}{2}$$ about (8, 4)
A translation by $$\begin{pmatrix} -1.5 \\ 0 \\ \end{pmatrix}$$
A translation by $$\begin{pmatrix} 3 \\ 0 \\ \end{pmatrix}$$