AP
T ER
CH
11
Transformations
1. State the transformation involved if P′ is the image of P. Q P
P′
2. For the diagram given, figure Q′ is the image of Q under a transformation. State (a) the transformation involved (b) the image of point R M
N Q
U
R S
V Q′ W X
3. Based on the given transformation, draw the images or the objects for each of the following. (a) K ′ is the image of K when K is reflected about the line RS. R
K S
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(b) K ′ is the image of K that was rotated 270° about point B in an anticlockwise direction. K′ B
4. State whether the following represents a translation or not. Write either “u” or “2” in the box given. C
C′
5. Draw the image of the following translation represented by the direction line RS.
A
R
S
6. Draw the image of the object under the translation y 6 4 2 0
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x 2
4
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6
–4
1 3 2.
7. State the direction and the distance of the movement of the following translation. N
N′
8. Given that A′ is the image of A under a translation. Write the translation in the form a 1 b 2. A
A′
9. Find the coordinates of the image of point B(–2, 3) under translation 10. Find the coordinates of the object of point Q′(7, 9) for translation
6
1 –4 2 .
–3
1 8 2.
–2 5 11. A point, Q, is under a translation of 1 2 and then 1 2 . The final image of Q is (7, 4). 3 –1 (a) Determine the coordinates of Q. (b) State the equivalent single translation for Q. 12. Draw the image of the given object under a reflection about line PQ. P
Q
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13. For the following object and its image, construct the axis of reflection, RS.
14. Given that N′ is the image of N under a reflection. Describe the reflection completely. E
H N′
D
F
C
A
N G
B
15. For each of the points A, B, C and D shown in the diagram, mark the images obtained when the points are reflected about y-axis. Hence, state the coordinates of the images. Coordinates of point
y 5
A
4 3
B
(a)
A(2, 4)
(b)
B(–2, 2)
(c)
C(–1, –3)
(d)
D(1, 1)
Coordinates of image
2 1
–4 –3 –2 –1 0 –1
D 1
–2 C
2
3
4
5
x
–3 –4
16. A point K(3, −4) is mapped to its image K′ under a reflection about x-axis. K′ is then mapped to K′′ under a reflection about the y-axis. (a) State the coordinates of K′′. (b) Describe one reflection which maps K to K′′.
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17. Draw the image of the object under a rotation through 90° anticlockwise about the centre O. O
B
18. M′ is the image of M under a rotation. Mark the centre of rotation as O in the diagram and hence, state the angle and direction of the rotation.
(a) Angle of rotation:
M′
(b) Direction:
M
19. Mark and state the coordinates of the images of points R and S under a rotation through 90° clockwise about the point (2, 3). y R
6 5 4 3 2 1 0
S 1
2
3
x 4
5
20. Mark and state the coordinates of the objects of points T′ and U′ under a rotation through 90° anticlockwise about the point (–2, 1). y 4 3 2 1 –5 –4 –3 –2 –1 0 –1
U′ 1
x
–2
T′
–3 –4
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21. Given S′ is the image of S under a rotation. Describe the rotation completely. H
I B
S
C D S′ A
G F
E
22. A point M(3, 1) is under a rotation through 90° anticlockwise about the point (0, −1). The image M′ is then mapped to M′′ under a rotation 180° about the point (1, 2). Find the coordinates of M′ and M′′. 23. State whether the following transformation is an isometry.
24. In the diagram, complete the pattern by drawing the images of the object under a 2 translation 1 2 three times. 0 y
x
0
25. State whether the following pair of diagrams are congruent.
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26. P
3 cm
S 5 cm
Q
R
Parallelogram PQRS experiences a reflection along the line QR. Calculate the perimeter of the whole diagram formed. 27. I M J
Q
L P
O
K
N
IJKL is a rectangle with sides 5 units and 3 units respectively. M, N, P and Q are midpoints of the respective sides. (a) ∆OKL is the image of ∆IJO under a rotation through about the point . (b) The midpoint of diagonals JL and IK is point (c) ∠IOJ =
and ∠IOL =
. .
(d) The perimeter of IJKL = (e) The area of ∆IJL = The area of (f)
.
.
A rectangle like IJKL has
axes of symmetry.
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