Identifying multiple transformations
I can identify what transformations have taken place.
- Year 10
Identifying multiple transformations
I can identify what transformations have taken place.
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.
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.A vector can be used to describe a __________.
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''.
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''.
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?
Q5.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
Q6.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 $$(4, 1)$$
Assessment exit quiz
6 Questions
Q1.A point on a shape is __________ if that point has not changed location after the shape is transformed.
Q2.Select the information you should give to fully describe a rotation.
Q3.What type of transformation maps shape A onto shape B?
Q4.Describe one possible transformation from A to B that has zero invariant points.
Q5.Describe the transformation that maps shape A onto shape E.
Q6.Select the two transformations needed to map shape A onto shape C.
