Paper-1

1 The diagram below shows triangle A and triangle B. For

Examiner’s
(a) Describe fully the single transformation that maps triangle A onto triangle B. Use

Answer (a) ................................................................................................................................

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

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

(b) Triangle A is mapped onto triangle C by a rotation, centre the origin, through 90° anticlockwise.

(i) Draw, and label, triangle C on the diagram.

Answer (b)(i)

y
3

2
A
1

–3 –2 –1 0 1 2 3x
–1

–2
B
–3

–4
[1]

(ii) Write down the matrix that represents this transformation.

Answer (b)(ii) [1]

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2 The diagram below shows three triangles, P, Q and R. For

Examiner’s
(a) Triangle T is the image of triangle P under an enlargement with centre (5, 2) and scale Use

factor 2.

Draw and label triangle T on the diagram.

Answer (a)

5
Q
4
P
3

–5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1

–2

–3

–4
R
–5

–6
[2]

(b) Describe fully the single transformation that maps triangle P onto triangle Q.

Answer (b) ................................................................................................................................

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

(c) Find the matrix representing the transformation that maps triangle Q onto triangle R.

Answer (c) 冢 冣 [1]

© UCLES 2010 4024/12/M/J/10

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3 The diagram shows triangle ABC. For

y Examiner’s
Use

B ( 2, 4 )

A ( –4, 1 ) C ( 2, 1 )

O x

Triangle ABC is translated by  92 onto triangle AʹBʹCʹ.

(a) Find the coordinates of Cʹ.

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

(b) What special type of quadrilateral is BCCʹBʹ ?

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

(c) Find the area of quadrilateral BCCʹBʹ .

Answer .......................... units2 [2]

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4 The diagram shows two triangles, A and B. For

Examiner’s
Use
y
7

2
A
1

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

–2
B
–3

–4

–5

–6

–7

(a) Write down the vector that represents the translation that maps triangle A onto triangle B.

Answer [1]

(b) Triangle C is an enlargement of triangle A with centre (5, 3) and scale factor 3.

Draw and label triangle C. [2]

© UCLES 2012 4024/12/M/J/12 [Turn over

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5 For
y Examiner’s
Use
4

3
A
2

1
B
–4 –3 –2 –1 0 1 2 3 4 x
–1

–2

–3

–4

The diagram shows triangles A and B.

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

Answer ......................................................................................................................................

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

(b) Triangle A is mapped onto triangle C by the transformation T.

T is a rotation, centre the origin, through 270° clockwise.

(i) On the diagram, draw triangle C. [1]

(ii) Find the matrix that represents T.

Answer f p [1]

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6 The diagram shows triangles A and B and the point P (0, 4). For
Examiner’s
y Use

5
P
4

2
B A
1

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 x

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

Answer .......................................................................................................................................

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

(b) Triangle A is mapped onto triangle C by an enlargement, centre P, scale factor - 21 .

On the diagram, draw triangle C. [2]

area of triangle A
(c) Find the value of .
area of triangle C

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

Question 26 is printed on the following page.

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7
y

A B

O x

A is the point (1, 7) B is the point (6, 7)

J 0N
The line AB is mapped onto the line PQ by the translation K O .
L- 5P
(a) Find the coordinates of Q.

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

(b) What special type of quadrilateral is ABQP?

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

(c) Find the area of the quadrilateral ABQP.

Answer ................................... units2 [1]

© UCLES 2015 4024/11/M/J/15

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y
5

3
B
2
A
1

–5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1

–2

–3

–4

–5

–6

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

Answer ...............................................................................................................................................

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

(b) Triangle A is mapped onto triangle C by an enlargement, centre (0, 2) and scale factor -2.

Draw, and label, triangle C on the diagram. [2]

© UCLES 2016 4024/11/O/N/16 [Turn over

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9 The diagram shows triangles A and B.

2
A
1

x
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
–1

–2

–3
B
–4

–5

–6

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

Answer ...............................................................................................................................................

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

(b) Triangle A is mapped onto triangle C by a rotation, 90° anti-clockwise about the origin.

On the diagram, draw triangle C. [2]

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10 (a) Triangle A is shown on the grid.

y
10

2
A
1

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

–2

–3

–4

–5

–6
J 7N
(i) Triangle A is mapped onto triangle B by a translation of KK OO .
L- 5P
Draw and label triangle B on the grid. [2]

(ii) Triangle A is mapped onto triangle C by an enlargement scale factor -2, centre (-1, 2).

Draw and label triangle C on the grid. [2]

© UCLES 2017 4024/22/O/N/17

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11
y

4
B
3

1
A
0
1 2 3 4 5 6 7 8 9 10 11 x
–1

–2

–3

–4

–5

Triangle A is mapped onto triangle B by a translation, followed by an enlargement with centre (10, –4).
The translation maps triangle A onto triangle C.
The enlargement maps triangle C onto triangle B.

(a) Write down the scale factor of the enlargement.

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

(b) Draw triangle C on the grid. [2]

(c) Find the column vector that represents the translation that maps triangle A onto triangle C.

Answer f p [1]

Question 25 is printed on the next page

© UCLES 2018 4024/12/M/J/18 [Turn over

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12 The diagram shows triangle A and triangle B.

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

–2

–3
A
–4

–5
B
–6

–7

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

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

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

(b) Triangle A is mapped onto triangle C by a rotation, 90° anticlockwise, centre (0, 0).

Draw triangle C. [2]

(c) Triangle A is mapped onto triangle D by an enlargement, scale factor 3, centre (5, -5).

Draw triangle D. [2]

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13
y
6

3
B
2

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

–3

–4

–5

–6

Triangle A and triangle B are drawn on the grid.

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

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

..................................................................................................................................................... [3]
1
f 1 p.
- 0
2
(b) Transformation P is represented by the matrix
0 -
2
P maps triangle A onto triangle C.

On the grid, draw triangle C.

[2]

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14
y
6
5
4
3
B A
2
1

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

Triangles A, B and C are drawn on the grid.

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

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

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

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

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

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

(c) Triangle D is the image of triangle A after an enlargement, scale factor 2, with
centre of enlargement (1, 2).

Draw triangle D. [2]

© UCLES 2021 4024/11/M/J/21 [Turn over

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15
y

5
B
4

3
A
2

–5 –4 –3 –2 –1 0 1 2 3 4 5 x
–1

–2

–3

–4

Triangle A and triangle B are drawn on the grid.

(a) Complete the description of the transformation that maps triangle A onto triangle B.

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

(b) Triangle A is mapped onto triangle C by a reflection in the line y =- x .

On the grid, draw and label triangle C. [2]

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Q R S
1 (a) PQRS and PQRS are congruent quadrilaterals.
R is the same point as S.
S is the same point as R. P
P
A single transformation maps P onto P,
Q onto Q, R onto R and S onto S.
S R Q

(i) Describe fully this transformation. [3]

(ii) Write down two facts connecting PQ and QP. [1]

(b) (Extra)
y

4
B
3

1
A
0 1 2 3 4 5 6 x

The diagram shows triangle A and triangle B.

(i) A translation, T, maps triangle A onto triangle B.

State the column vector representing this translation. [1]

(ii) The transformation, S, that maps triangle A onto triangle C is represented by the
matrix 冢2
0
0
1 冣
.

Find the vertices of triangle C. [2]

(iii) Given that TS(A) = D, find the vertices of triangle D. [1]

(iv) Triangle E has vertices (0,0), (2,0) and (0,3).

(a) It is given that (0,0) (0,0), (1,0) (2,0) and (0,1) (0,3).

Find the matrix that represents this transformation. [2]

(b) Describe fully the single transformation that maps triangle A onto triangle E. [2]

© UCLES 2010 4024/22/O/N/10

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x Do not

 3 –1 0
  
11 = 4 . write in this
2 (a) margin
1 –0 1 y 9
(Extra) Find x and y.

Answer x = ................................ [2]

y = ................................ [2]

2 (b) (i) The transformation A is represented by the matrix

a
c
b
d.

Find, in terms of a, b, c and d as appropriate,

(a) the image of (1, 0) under the transformation A,

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

(b) the image of (0, 1) under the transformation A.

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

© UCLES 2011 4024/22/O/N/11

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(ii) The transformation B maps (1, 0) onto (1, 3) and (0, 1) onto (–3, –2). Do not
write in this
Write down the matrix that represents transformation B. margin

Answer
  [1]

(iii) Describe fully the transformation given by the matrix

10 –10 .

Answer ...............................................................................................................................

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

© UCLES 2011 4024/22/O/N/11 [Turn over

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3 (a) Some transformations of the plane are given in the following table. Do not
write in this
margin
Mx Reflection in the x-axis
My Reflection in the y-axis
Md Reflection in the line y = –x
R90 Rotation of 90°, anti-clockwise, centre the origin
R180 Rotation of 180°, centre the origin
R270 Rotation of 270°, anti-clockwise, centre the origin.

You may use the grid on the next page to help answer the following questions.

(i) The point A has coordinates (2, 3).

(a) Find the coordinates of My(A).

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

(b) Find the coordinates of Md My(A).

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

(c) The inverse of R90 maps B onto A.

Find the coordinates of B.

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

(ii) (a) Write down the matrix which represents Mx.

Answer ( ) [1]

(b) Which single transformation given in the table is equivalent to R180Mx?

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

© UCLES 2011 4024/21/O/N/11
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Do not
write in this
margin

Turn over for the rest of this question.

© UCLES 2011 4024/21/O/N/11 [Turn over

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(b) The points P and Q have coordinates (4, 0) and (9, 0) respectively. Do not
The points P´ and Q´ have coordinates (4, 4) and (7, 8) respectively. write in this
margin

(i) Write down the length of PQ.

Answer PQ = ..................... units [1]

(ii) Calculate the length of P´Q´.

Answer P´Q´ = .................... units [2]

(iii) PQ is mapped onto P´Q´ by a single rotation.

By using the grid below,

(a) find, by drawing, the coordinates of the centre of this rotation,

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

(b) measure the clockwise angle of rotation.

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

y
8

–2 0 2 4 6 8 10 x

–2

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2011 4024/21/O/N/11

 Paper-2

4 (a) The diagram shows triangles A, B and C. Do not

write in this
y margin
6

2
A
1

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

–2

–3
C
B
–4

–5

–6

(i) Describe fully the single transformation that maps

(a) triangle A onto triangle B,

Answer ......................................................................................................................

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

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

(b) triangle A onto triangle C.

Answer ......................................................................................................................

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

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

© UCLES 2011 4024/21/M/J/11

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(ii) One vertex of triangle A is (2, 1). Do not

write in this
Find the coordinates of this point when it is margin

(a) reflected in the line y = –x,

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

(b) rotated through 90° anticlockwise about (1, –1).

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

(b) You may use the grid below to help you answer this question.

The points (2, 1), (4, 3), (3, 1) and (p, q) form a quadrilateral.
This quadrilateral has rotational symmetry order 1 and one line of symmetry.

(i) One possible position of (p, q) is (2, 2).

Write down the name of this special quadrilateral.

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

(ii) Given that p and q are integers, find two other possible positions of (p, q).

Answer (........... , ...........)

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

y
5

0
0 1 2 3 4 5 x

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5 Do not
y write in this
margin
8

3
A
2

í5 í4 í3 í2 í1 0 1 2 3 4 5 x
í1
L
í2

The diagram shows triangle A and line L.

(i) Triangle A is mapped onto triangle B by a reflection in line L.

Draw and label triangle B. [2]

(ii) Triangle A is mapped onto triangle C by an anticlockwise rotation of 90°, centre (0, 3).

Draw and label triangle C. [2]

(iii) Triangle C is mapped onto triangle D by a reflection in line L.

Describe the single transformation that maps triangle B onto triangle D.

Answer ..............................................................................................................................

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

© UCLES 2012 4024/22/O/N/12

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6 (a)

y
6

5
A
4

3
B
2

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

–2

–3

–4

–5

–6

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

Answer .......................................................................................................................................

............................................................................................................................................... [2]
J- 2N
(ii) Triangle B is mapped onto triangle C by a translation, vector K O .
L- 3P
Draw and label triangle C. [2]

(iii) Triangle A is mapped onto triangle D by a reflection in the line y = x .

Draw and label triangle D. [2]

(iv) Triangle E is geometrically similar to triangle A and its longest side is 12 cm.

Calculate the area of triangle E.

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

© UCLES 2015 4024/22/M/J/15

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7 y

4
A

x
–8 –4 0 4 8

–4

J- 3N
(i) Flag A is mapped onto flag T by the translation K O .
L- 6P
Draw, and label, flag T. [1]

(ii) Describe fully the enlargement that will map flag A onto flag B.

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

(iii) Find the centre of the rotation that will map flag A onto flag C.

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

(iv) Rotate flag B through 45° anticlockwise about the origin.

Label the image R. [2]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable
effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will
be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International
Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after
the live examination series.

Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2015 4024/22/O/N/15

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8 Triangles A, B, C and D are drawn on a centimetre square grid.

y
6

4
B
3

1
A

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

–3
C
–4

–5

–6

(a) The perimeter of triangle A is ^a + bh cm, where a and b are integers.

Find a and b.

Answer a = ............... b = .............. [2]

(b) Triangle A is mapped onto triangle B by the translation T.

Write down the column vector that represents T.

J N
K O
Answer KK OO [1]
L P
(c) Describe fully the single transformation that maps triangle B onto triangle C.

Answer .............................................................................................................................................

....................................................................................................................................... [2]
© UCLES 2016 4024/22/M/J/16
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(d) Describe fully the single transformation that maps triangle B onto triangle D.

Answer .............................................................................................................................................

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

(e) Write down the matrix that represents the transformation which maps triangle D onto triangle A.

Answer [1]

(f) The transformation V is a reflection in the line y = 0.

The transformation W is a rotation 90° clockwise about (0, 0).
The single transformation X is equivalent to the transformation V followed by the
transformation W.

(i) The point (g, h) is mapped onto the point P by the transformation X.

Find the coordinates of P.

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

(ii) Describe fully the single transformation X.

Answer .............................................................................................................................................

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

© UCLES 2016 4024/22/M/J/16 [Turn over

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9 The grid shows triangles A and B and rectangle R.

y
6

3
A R
2

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1

–2

–3
B
–4

–5

–6

(a) Triangle A is mapped onto triangle B by the single transformation K.

Find the matrix representing transformation K.

Answer f p [2]

(b) Triangle B is mapped onto triangle C by a reflection in the y-axis.

On the diagram, draw triangle C. [1]

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(c) Triangle A is mapped onto triangle C by the single transformation L.

Describe fully the single transformation L.

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

J- 2N
(d) Rectangle R is mapped onto rectangle S by a translation by the vector KK OO .
L 3P
On the diagram, draw rectangle S. [2]

© UCLES 2018 4024/21/M/J/18 [Turn over