GCSE
Mathematics
Targeting Grade C
Shape and Space
Unit 6 Transformations
Can you ...
If not you need
Understand the 4 transformations
TOP The 4 transformations
• Understand Reflection
Practice 1 Reflection
• Understand Rotation
Practice 2: Rotation
Try a test
• Understand Enlargement
TAIL 1
Practice 3: Enlargement
• Understand Translation
Practice 4: Translation
Try a test
TAIL 2
TOP
Remember: There are 4 different types of transformations
Reflection – (mirror image) requires a mirror line, line
of symmetry or equation of the line of symmetry
Rotation – shape turns round but stays the same size;
requires the degree and direction of the rotation with a
point which is the centre of rotation
Enlargement – shape changes size (smaller or
larger); requires a scale factor and sometimes a
centre of enlargement
Translation – this is simply a shift and requires number
of units to be moved left/right and up/down
Lesson
Practice 1: Reflection
1.
y
O
Reflect the triangle in the x-axis.
x
(Total 1 mark)
Next
Practice 1: Reflection
A quadrilateral is shown on the grid.
2.
y
10
9
8
7
6
5
4
A
B
3
2
1
O
(a)
(b)
(c)
1
2
3
4
5
6
7
8
9
10 x
Write down the mathematical name of this quadrilateral.
Reflect the quadrilateral in the line AB.
Write down the coordinates of the point B.
(1)
(2)
(1)
(Total 4 marks)
Next
Practice 1: Reflection
3.
(a)
(b)
Triangle A and triangle B have been drawn on the grid.
Reflect triangle A in the line x = 3.
Label this image C.
(2)
Describe fully the single transformation which will map triangle A onto triangle B.
(2)
(Total 4 marks)
Lesson
Practice 2: Rotation
y
5
1.
4
3
A
2
1
–5
–4
–3
–2
–1 O
1
2
3
4
5
x
–1
–2
–3
–4
–5
(a) On the grid, rotate triangle A 180° about O.
Label your new triangle B.
(2)
Next
Practice 2: Rotation
y
2.
4
3
B
2
A
1
C
–5
–4
–3
–2
–1
O
x
1
2
3
4
5
–1
–2
–3
–4
(a)
(b)
Shape A is rotated 90° anticlockwise, centre (0, 1), to shape B
Shape B is rotated 90° anticlockwise, centre (0, 1), to shape C
Shape C is rotated 90° anticlockwise, centre (0, 1), to shape D
Mark the position of Shape D
Describe the single transformation that takes shape C to shape A.
(2)
(2)
(Total 4 marks)
Next
Practice 2: Rotation
y
3.
7
6
5
T
4
3
2
1
–7
–6
–5
–4
–3
–2
–1 0
1
2
3
4
5
6
7
x
–1
–2
–3
–4
–5
–6
–7
Rotate triangle T through 90° clockwise about the point (2, 1).
Lesson
(Total 2 marks)
TAIL 1
y
1.
A
R
x
O
B
(a) Reflect triangle R in the line AB.
Label the new triangle S.
(b) Rotate triangle R a half turn about the point O.
Label the new triangle T.
(1)
(2)
(Total 3 marks)
Next
TAIL 1
Here are four road signs.
2.
A
B
30
C
D
Two of these road signs have one line of symmetry.
(a) Write down the letters of each of these two road signs.
Only one of these four road signs has rotational symmetry.
(b) (i) Write down the letter of this road sign.
(ii) Write down its order of rotational symmetry.
(2)
(2)
(Total 4 marks)
Next
TAIL 1
3.
(a)
(b)
(c)
Find the area of the shaded shape
Find the perimeter of the shaded shape.
Reflect the shaded shape in the dotted line.
(2)
(1)
(2)
(Total 5 marks)
Next
TAIL 1
4.
(a)
(b)
Reflect triangle P in the line AB.
Label the new shape Q.
Rotate triangle P 1 turn clockwise, centre O.
(1)
4
Lesson
Label the new shape R.
(2)
(Total 3 marks)
Practice 3: Enlargement
1.
Q
(b) Enlarge shape Q by a scale factor of 2.
(2)
(Total 3 marks)
Next
Practice 3: Enlargement
2.
3 cm
Diagram NOT
accurately drawn
2 cm
(a) Work out the area of the rectangle
The rectangle is enlarged by a scale factor 2.
(b) Work out the area of the enlarged rectangle.
(1)
(2)
(Total 3 marks)
Next
Practice 3: Enlargement
3.
On the grid, enlarge the shape with a scale factor of 2.
Lesson
(2 marks)
Practice 4: Translation
P
(a)
Lesson
Translate shape P 3 squares to the left and 2 squares down.
(1)
TAIL 2
1.
Draw an enlargement, scale factor 3, of the shaded shape.
(Total 2 marks)
Next
TAIL 2
2.
y
7
6
5
4
3
2
1
–4
–3
–2
–1
O
1
2
3
4
5
6
7
8
x
–1
–2
–3
–4
Enlarge the shaded triangle by a scale factor 2, centre 0.
(Total 3 marks)
Next
TAIL 2
y
6
3.
5
Q
4
3
P
2
1
–3
–2
–1
O
1
2
3
4
5 x
–1
–2
Lesson
(i)
Describe fully the single transformation that maps shape P onto shape Q.
(ii)
Reflect shape P in the line x = 1
(Total 5 marks)