12
17 The diagram shows triangles A, B and C.
y
7
3
B
2
C A
1
x
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
(a) Triangle A can be mapped onto triangle B by a translation.
Write down the column vector for the translation.
Answer f p [1]
(b) Find the matrix representing the transformation that maps triangle A onto triangle C.
Answer f p [1]
(c) Triangle A is mapped onto triangle D by an enlargement, scale factor 2, centre ^5, 0h.
Draw and label triangle D. [2]
© UCLES 2014 4024/12/M/J/14
18
10 (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
24
(b) 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
16
10 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
17
(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
5
3.98 # 602.3
6 By making suitable approximations, estimate the value of .
2.987
Show clearly the approximations you use.
Answer .......................................... [2]
7
y
6
3
A
2
–2 –1 0 1 2 3 4 5 6 7 8 x
The diagram shows triangle A.
Triangle A is mapped onto triangle B by an enlargement.
The enlargement has centre (3, 3) and scale factor -2.
Draw and label triangle B. [2]
© UCLES 2016 4024/12/O/N/16 [Turn over
9
13 Triangle ABC is mapped onto triangle AlBlC l by a rotation, centre O, through 110° clockwise.
Draw and label triangle AlBlC l .
A B O
[3]
© UCLES 2016 4024/12/O/N/16 [Turn over
10
15 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]
© UCLES 2017 4024/12/M/J/17
8
4 (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
