y

1
8

3
A
2

í5 í4 í3 í2 í1 0 1 2 3 4 5 x
í1
L
í2

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

Draw and label triangle C. [2]

2 The diagram shows triangles A and B.
Triangle A is mapped onto triangle B by an anticlockwise rotation.
(i) Write down the angle of rotation.
(ii) Find the coordinates of the centre of rotation.

3
A
2

1
B

–2 –1 0 1 2 3 4 5 6 x
3 The diagram shows triangle A�
y
7

3
A
2

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

–2

–3

–4

Rotate triangle A through 90° clockwise about the point (–1, 3)�
Label the image C� [1]
4 The diagram below shows three triangles, P and Q.

5
Q
4
P
3

–5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1

–2

–3

–4

–5

–6

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

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

............................................................................................................................................. [2]
5 Q R S
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]

6 The diagram shows triangles A, B, C and D.

y
4

3
D
2
B
1
C

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

–3

Describe fully the single transformation that maps ∆C onto ∆D. [2]
 y
4

7 The single transformation Q maps 3

A
∆A onto ∆C. C 2
Describe, fully, the transformation Q. 1

–3 –2 –1 0 1 2 3 x
[2]

8 Describe fully the single transformation that maps triangle B onto triangle C. [2]
y

6
B
4

–6 –4 –2 0 2 4C 6 x
–2

–4 D
A
–6

y
9 The diagram shows shapes A and B. 8
Shape B is mapped onto shape C
by a rotation, centre (8, 3), through 90° clockwise.
Draw shape C on the diagram. 6

2
A B

0 2 4 6 8 x
[2]
 10 y

5
4
3
2
T
1

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 x
–1
–2
–3
B
–4
–5
–6
Describe fully the single transformation which maps ∆T onto ∆B. [2]

11 B

A'

20

55°
A 20 C B'

In triangle ABC, BÂC = 90°, BĈA = 55° and AC = 20 cm.

The triangle initially stood with AC on a horizontal surface.
It was then rotated about the point C onto triangle A
B
C, where ACB
is a straight line.
(a) Calculate
(i) the length of BC, [2]
(ii) the distance AB
, [1]
(iii) the height of A
above CB
. [2]
(b) Describe fully the path which the point A followed under this rotation. [2]

(c) Calculate the length of the path which the point A followed under this rotation. [2]
12
y
4

3
C
2

1 B
A

–4 –3 –2 –1 0 1 2 3 4 x
F D
–1

–2

–3
E
–4

Triangle ABC has vertices A (1, 1), B (3, 1) and C (1, 2).
Triangle DEF has vertices D (–1, –1), E (–1, –3) and F (–2, –1).

The matrix P represents the single transformation, T, that maps triangle ABC onto triangle DEF.

(i) Describe T fully. [2]

(ii) Write down the matrix P. [1]