- Year 10
Multiple transformations
I can carry out multiple transformations on a shape.
Lesson details
Key learning points
- A shape can be transformed more than once.
- The first transformation is performed on the object.
- The second transformation is performed on the image.
- The third transformation is performed on the new image etc.
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.
Polygon - A polygon is a flat (2D), closed figure made up of straight line segments.
Common misconception
The number of spaces to translate a shape can be worked out by counting the squares on the grid.
If there are axes, then it is important to check the scales. The length of one square does not always represent one unit.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.The is the starting figure before a transformation has been applied.
Q2.Match each description to the correct vector.
1 left and 2 down - $$\begin{pmatrix} -1 \\ -2 \\ \end{pmatrix}$$
1 right and 2 up - $$\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}$$
2 right and 1 up - $$\begin{pmatrix} 2 \\ 1 \\ \end{pmatrix}$$
2 right and 1 down - $$\begin{pmatrix} 2 \\ -1 \\ \end{pmatrix}$$
2 left and 1 up - $$\begin{pmatrix} -2\\ 1 \\ \end{pmatrix}$$
1 right and 2 up - $$\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}$$
Q3.The object has been transformed into the image. The type of transformation shown by the diagram is a .
Q4.Which of these diagrams show a rotation?
Q5.Shape c has been rotated 90° anti-clockwise about (-2, 2). The image is shape .
Q6.The point P has coordinates (-2, 3). P is reflected in different lines of reflection. Match the coordinates of the image of P to the equation of the line of reflection.
P'(-2, -3) - $$x= 0$$
P'(2, 3) - $$y = 0$$
P'(-3, 2) - $$y=-x$$
P'(3, -2) - $$y=x$$
Assessment exit quiz
6 Questions
Q1.A can be used to describe a translation.
Q2.Aisha reflects shape A in the line $$y=4$$ to A'. She then reflects A' in the line $$x=4$$ to A''. Select the coordinates of P' and P''.
Q3.Jun translates shape A by $$\begin{pmatrix} 2 \\ -1 \\ \end{pmatrix}$$ to A'. He then reflects A' in the line $$x=5$$ to A''. Select the coordinates of P' and P''.
Q4.Sam is using technology to transform some shapes. Sam wants to use Desmos to rotate a shape 90° clockwise. Which of these angles should Sam type into Desmos?
Q5.Here are some buttons that you can use in Desmos for transformations. Match each button to its function.
Button a - translates object
Button b - rotates object
Button c - enlarges (dilates) object
Button d - creates a polygon
Q6.Match each transformation to its description.
Shape A to shape B - Rotation $$90$$° clockwise about $$(4, 1)$$
Shape B to shape C - Translation by $$\begin{pmatrix} -4 \\ -5 \\ \end{pmatrix}$$
Shape C to shape D - Reflection in the line $$x=4$$
Shape D to shape E - Enlargement, scale factor $$2$$, about $$(6,-3)$$
