1

1
y
9

8
T
7

3
P
2

1 3 4 5 6 7 8 9 10 11 x
2
0

Describe fully the single transformation that maps triangle T onto triangle P.

....................................................................................................................................................................

.................................................................................................................................................................... [3]

[Total: 3]

2 The grid shows triangles A, B and C.

 2

y
8
7
6
5
4
3
B
2
A
1

0 x
–6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8
–1
C
–2
–3
–4
–5
–6
–7
–8

(a) Describe fully the single transformation that maps triangle A onto triangle B.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(b) Describe fully the single transformation that maps triangle A onto triangle C.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(c) Draw the image of

(i) triangle A after a translation by the vector , [2]

(ii)
triangle A after a reflection in the line y = −2. [2]

[Total: 10]

3 The grid shows three shapes, A, B and C.

 3

(a) Describe fully the single transformation that maps

(i) shape A onto shape B,

................................................................................................................................................

................................................................................................................................................ [2]

(ii) shape A onto shape C.

................................................................................................................................................

................................................................................................................................................ [3]

(b)
On the grid, draw the image of shape A after a rotation, 90° clockwise, centre (6, −3). [2]

[Total: 7]
 4

4
y
6

3
A
2

–5 5 6 7 x
–4 –3 –2 –1 1 2 3 4
0
–1

–2

–3

–4

–5

On the grid, draw the image of

(a) triangle A after a reflection in the y-axis, [1]

(b) triangle A after a translation by the vector . [2]

[Total: 3]
 5

5
y
6
5
4
3
A
2
1
B
–5 5 6 7 8 9 10 x
–4 –3 –2 –1 1 2 3 4
0
–1
–2
–3
–4
–5

Describe fully the single transformation that maps triangle A onto triangle B.

....................................................................................................................................................................

.................................................................................................................................................................... [3]

[Total: 3]

6
The diagram shows three quadrilaterals, A, B and C, on a 1 cm2 grid.
 6

y
11

10

8
B
7
w
6

3
A
2
C
1

x
0
–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7
–1

–2

–3

–4

(a) (i) Write down the mathematical name for quadrilateral B.

................................................... [1]

(ii) Work out the area of quadrilateral B.

Give the units of your answer.

.............................. .................... [3]

(b) Measure angle w.

Angle w = ................................................... [1]

 7

(c) Describe fully the single transformation that maps

(i) quadrilateral A onto quadrilateral B,

................................................................................................................................................

................................................................................................................................................ [3]

(ii) quadrilateral A onto quadrilateral C.

................................................................................................................................................

................................................................................................................................................ [3]

[Total: 11]

7
y

10

2
C

x
–8 –6 –4 –2 0 2 4 6 8 10

–2

–4

–6
A
B

–8

–10

(a) Describe fully the single transformation that maps

 8

(i) triangle A onto triangle B,

.............................................................................................................................................

............................................................................................................................................. [3]

(ii) triangle A onto triangle C.

.............................................................................................................................................

............................................................................................................................................. [3]

(b) Draw the image of triangle A after a translation by the vector . [2]

[Total: 8]

8
y
8

T
2

–8 –6 –4 –2 0 2 4 6 8
x

–2

–4

A
–6

–8

(a) Describe fully the single transformation that maps triangle T onto triangle A.

..........................................................................................................................................................

.......................................................................................................................................................... [2]

(b) Draw the image of triangle T after an enlargement, scale factor , centre (0, 0). [2]

[Total: 4]
 9

The diagram shows four polygons on a 1 cm2 grid.

y
11

10

9
A
8

4
C
3

x
0
–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7
–1

–2

–3

–4
B
–5

–6

–7

–8
 10

(a) Write down the mathematical name of the shaded polygon.

................................................... [1]

(b) Find the area of the shaded polygon.

................................................... cm2 [2]

(c) Describe fully the single transformation that maps

(i) the shaded polygon onto polygon A,

................................................................................................................................................

................................................................................................................................................ [2]

(ii) the shaded polygon onto polygon B,

................................................................................................................................................

................................................................................................................................................ [3]

(iii) the shaded polygon onto polygon C,

................................................................................................................................................

................................................................................................................................................ [3]

(d) On the grid, draw the image of the shaded polygon after a reflection in the line y = 0. [2]

[Total: 13]

10
The diagram shows three triangles, A, B and C, on a 1 cm2 grid.
 11

y
4

3
C
2

–9
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5
–1

–2
B
–3

–4
A
–5

–6

–7

(a) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

................................................................................................................................................

................................................................................................................................................ [3]

(ii) triangle A onto triangle C.

................................................................................................................................................

................................................................................................................................................ [3]

(b) On the grid, draw the image of

(i) triangle A after a translation by the vector , [2]

(ii)
triangle A after a reflection in the line x = −4.5 . [2]
 12

(c) The diagram also shows an angle b in triangle B.

Use trigonometry to show that angle b is 63.4°, correct to 1 decimal place.

[2]

[Total: 12]

11 The diagram shows three triangles A, B and C on a grid.

Triangle A is shaded.
 13

y
11

10

7
w
6

4
A
3
B
2

x
0
–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7
–1

–2

–3
C
–4

–5

–6

–7

–8

–9
 14

(a) Measure angle w.

Angle w = ................................................... [1]

(b) Explain why triangle B is congruent to triangle C.

.......................................................................................................................................................... [1]

(c) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

................................................................................................................................................

................................................................................................................................................ [3]

(ii) triangle B onto triangle C.

................................................................................................................................................

................................................................................................................................................ [3]

(d) On the grid, draw the image of

(i) triangle A after a translation by the vector , [2]

(ii)
triangle A after a reflection in the line y = −1. [2]

[Total: 12]
 15

12
y

14

12

10
B

8
A

x
0
–14 –12 –10 –8 –6 –4 –2 2 4 6 8 10

–2

–4

C
–6

–8

–10

(a) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

................................................................................................................................................

................................................................................................................................................ [3]

(ii) triangle A onto triangle C.

................................................................................................................................................

................................................................................................................................................ [3]

(b) Draw the image of triangle A after a translation by the vector . [2]

(c) Draw the image of triangle A after a reflection in the line y = 4. [2]

[Total: 10]
 16

13

Describe fully the single transformation that maps shape A onto shape B.

....................................................................................................................................................................

.................................................................................................................................................................... [3]

[Total: 3]
 17

14

Describe fully the single transformation that maps triangle T onto triangle U.

....................................................................................................................................................................

.................................................................................................................................................................... [3]

[Total: 3]

15 The grid shows a point E and four quadrilaterals, A, B, C and D.

 18

(a) Write down the mathematical name of shape A.

................................................... [1]

(b) Describe fully the single transformation that maps

(i) shape A onto shape B,

................................................................................................................................................

................................................................................................................................................ [2]

(ii) shape A onto shape C,

................................................................................................................................................

................................................................................................................................................ [2]
 19

(iii) shape A onto shape D.

................................................................................................................................................

................................................................................................................................................ [3]

(c) (i) Write down the coordinates of the point E.

( .............................. , .............................. ) [1]

(ii) On the grid, draw the image of shape A after an enlargement by scale factor 3, centre E. [2]

[Total: 11]

16

(a) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

................................................................................................................................................

................................................................................................................................................ [3]
 20

(ii) triangle A onto triangle C,

................................................................................................................................................

................................................................................................................................................ [2]

(iii) triangle A onto triangle D.

................................................................................................................................................

................................................................................................................................................ [3]

(b)
On the grid, draw the image of triangle A after a reflection in the line y = −1. [2]

[Total: 10]

17

(a)
Draw the image of triangle T after a reflection in the line y = −1. [2]

(b) Draw the image of triangle T after a rotation through 90° clockwise about (0, 0). [2]
 21

(c) Describe fully the single transformation that maps triangle T onto triangle A.

..........................................................................................................................................................

.......................................................................................................................................................... [2]

[Total: 6]

18

(a) (i)
Draw the image of triangle A after a reflection in the line y = −x. [2]

(ii) Draw the image of triangle A after a translation by the vector . [2]

(b) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

................................................................................................................................................

................................................................................................................................................ [3]
 22

(ii) triangle A onto triangle C.

................................................................................................................................................

................................................................................................................................................ [3]

[Total: 10]

19

(a) Describe fully the single transformation that maps shape T onto shape A.

..........................................................................................................................................................

.......................................................................................................................................................... [2]

(b) On the grid, reflect shape T in the line y = x. [2]

[Total: 4]

20 Triangles A, B and C are shown on the grid.

 23

(a) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

................................................................................................................................................

................................................................................................................................................ [3]

(ii) triangle A onto triangle C.

................................................................................................................................................

................................................................................................................................................ [3]

(b) On the grid,

(i) translate triangle A by the vector , [2]

(ii) reflect triangle A in the line y = 1. [2]

[Total: 10]
 24

21

Describe fully the single transformation that maps

(a) triangle A onto triangle B,

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(b) triangle A onto triangle C.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

[Total: 6]

22
Three quadrilaterals are shown on a 1 cm2 grid.
 25

(a) Write down the mathematical name of the shaded quadrilateral.

................................................... [1]

(b) For the shaded quadrilateral

 26

(i) measure the perimeter,

................................................... cm [1]

(ii) work out the area.

................................................... cm2 [1]

(c) Describe fully the single transformation that maps the shaded quadrilateral onto

(i) quadrilateral A,

................................................................................................................................................

................................................................................................................................................ [2]

(ii) quadrilateral B.

................................................................................................................................................

................................................................................................................................................ [3]

(d) On the grid,

(i) reflect the shaded quadrilateral in the line x = 1, [2]

(ii) enlarge the shaded quadrilateral by scale factor , centre (−1, 0). [2]

[Total: 12]
 27

23

(a) Describe fully the single transformation that maps shape A onto shape B.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(b) Describe fully the single transformation that maps shape A onto shape C.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(c) On the grid, draw the image of shape A after a translation by the vector . [2]

(d) On the grid, draw the image of shape B after a reflection in the line y = 1. [2]

[Total: 10]

24
The diagram shows four shapes A, B, C and D and a point P on a 1 cm2 grid.
 28

(a) Find

(i) the perimeter of shape A,

................................................... cm [1]

(ii) the area of shape A.

................................................... cm2 [1]

(b) (i) Write down the co-ordinates of point P.

( .............................. , .............................. ) [1]

(ii) Find the co-ordinates of the image of point P when

 29

A P is reflected in the y-axis,

(.............................. , .............................. ) [1]

B P is reflected in the line y = 6.

( .............................. , .............................. ) [2]

(iii)
Find the vector that translates point P to the point (49, −12).

[2]

(c) Describe fully the single transformation that maps

(i) shape A onto shape B,

................................................................................................................................................

................................................................................................................................................ [3]

(ii) shape C onto shape D.

................................................................................................................................................

................................................................................................................................................ [3]

[Total: 14]
 30

25

(a)
Translate shape T by the vector .

Label the image A.

[2]

(b) Rotate shape T about the point (5, 3) through 180°.

Label the image B.
[2]

(c) Describe fully the single transformation that maps shape A onto shape B.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

[Total: 7]
 31

26

Reflect shape T in the line y = x. [2]

[Total: 2]
 32

27

(a) On the grid, draw the image of

(i) triangle A after a translation by the vector , [2]

(ii) triangle A after a reflection in the line y = x. [2]

(b) Describe fully the single transformation that maps triangle A onto triangle B.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

[Total: 7]
 33

28 Reflect this shape in the line AB.

[2]

[Total: 2]

29

Draw the enlargement of the triangle by scale factor 3, centre X. [2]

[Total: 2]
 34

30

(a) Describe fully the single transformation that maps

(i) triangle A onto triangle B,

................................................................................................................................................

................................................................................................................................................ [2]

(ii) triangle A onto triangle C.

................................................................................................................................................

................................................................................................................................................ [3]

(b) On the grid, draw the image of

(i) triangle A after an enlargement, scale factor , centre (3, 0), [2]

(ii) triangle A after a translation by the vector . [2]

[Total: 9]
 35

31 Shape A is shown on the grid.

On the grid, enlarge shape A by scale factor 3. [2]

[Total: 2]
 36

32

(a) Describe fully the single transformation that maps triangle A onto triangle B.

..........................................................................................................................................................

.......................................................................................................................................................... [2]

(b) On the grid, draw the image of triangle A after a reflection in the line . [2]

(c) On the grid, draw the image of triangle A after a rotation through 180° about (0, 0). [2]

[Total: 6]

33
Shapes A, B and C are shown on the 1 cm2 grid.
 37

(a) Shape A is a special type of quadrilateral.

Write down the mathematical name for shape A.

................................................... [1]

(b) Describe fully the single transformation that maps

 38

(i) shape A onto shape B,

................................................................................................................................................

................................................................................................................................................ [3]

(ii) shape A onto shape C.

................................................................................................................................................

................................................................................................................................................ [3]

(c) On the grid,

(i) translate shape A by the vector , [2]

(ii) reflect shape A in the line x = 2. [2]

(d) Find the area of shape B.

................................................... cm2 [1]

[Total: 12]

34 Triangles A, B and C are shown on the grid.

 39

(a) Describe fully the single transformation that maps triangle A onto triangle B.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(b) Describe fully the single transformation that maps triangle A onto triangle C.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(c) Translate triangle A by the vector . [2]

(d) Reflect triangle A in the line x = 3. [2]

[Total: 10]
 40

35

(a) Describe fully the single transformation that maps

(i) flag A onto flag B,

.............................................................................................................................................

............................................................................................................................................. [2]

(ii) flag A onto flag C,

.............................................................................................................................................

............................................................................................................................................. [3]

(iii) flag A onto flag D.

.............................................................................................................................................

............................................................................................................................................. [3]
 41

(b)
Draw the reflection of flag A in the line y = −1. [2]

[Total: 10]

36

(a) Describe fully the single transformation that maps triangle A onto triangle B.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(b) On the grid, draw the image of

(i) triangle A after a reflection in the x-axis, [1]

(ii) triangle A after a translation by the vector . [2]

[Total: 6]
 42

37

(a) Describe fully the single transformation that maps triangle T onto triangle P.

..........................................................................................................................................................

.......................................................................................................................................................... [2]

(b) Translate triangle T by the vector . [2]

(c) Rotate triangle T through 90° anticlockwise about (0, 0). [2]

(d) Enlarge triangle T by scale factor with centre (0, 0). [2]

[Total: 8]
 43

38 Enlarge the rectangle using a scale factor of 3 and centre of enlargement O.

[2]

[Total: 2]

39

(a) Describe fully the single transformation that maps triangle T onto triangle U.

..........................................................................................................................................................

.......................................................................................................................................................... [3]
 44

(b) On the grid, draw the image of triangle T after a rotation through 90° clockwise about the point
(7, 3).
[3]

[Total: 6]

40 The diagram shows three triangles A, B and C.

(a) Describe fully the single transformation that maps triangle A onto triangle B.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(b) Describe fully the single transformation that maps triangle A onto triangle C.

..........................................................................................................................................................

.......................................................................................................................................................... [3]

(c) Draw the image of

 45

(i) triangle A after a translation by the vector , [2]

(ii)
triangle A after a reflection in the line y = −3. [2]

[Total: 10]