chapter 2 i transformation i,ii enhance(2)

8/3/2019 Chapter 2 I Transformation I,II ENHANCE(2)

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Transformations I,II 13

1

Diagram 1 is drawn on a square grid. F

is the image of E under translation. StateThe coordinates of the image of C under the

same translation.

A. (3, 0) B. (3, -1)C. (4, 0) D. (4, -1)

2.

.

Diagram 2 is drawn on a square grid. Byconsidering the point labeled A, B, C and D, find

the image of Q under rotation 90oanticlockwise about P.

3.

Diagram 3 is drawn on a square grid. Given that

R and S are the images of R and S underrotation anticlockwise. The centre of rotation is

a coordinates

A. (0, 4) B. (1, 4)C. (1, 3) D. (2, 3)

4.

Diagram 4 shows triangle R and S on a squaregrid. R is the image of S under a rotation of 90o

anticlockwise. Which of the points A, B, C or Dis the centre of rotation?

-4 -2 0 2 4

4

4

2

-2

x

-4

Q

A

P

D

B

C

4

A

C

T

Diagram 4

D

BS

R

C

4

-2

4

2

0

E

F

x

Diagram 1

y

Diagram 2

y

-4 -2

y

4

x

4

2

-2

R'

S'R

S

T U

Diagram 3

-2 0 2 4

Question Basedon Examination Format


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5

In Diagram 5, Q is the image of P under a

rotation. The angle of rotation is

A. 90o

B. 120o

C. 180o D. 270o

6

Diagram 6 is drawn on a square grid.Triangle OPQ is under an enlargementat a centre O. Coordinates P' is the image of P .

Which point of A, B, C and D is the image of Qunder the same enlargement?

7. Diagram 7 shows points plotted on aCartesian plane.

Which of the point A, B, C and D is the image

of M under an anticlockwise rotation of 90o

about the centre (1,2 )

8.

The triangles in Diagram 8 are drawn in a squaregrid. Point S is the image of S under a certaintranslation. Which of the point A, B, C and D is

the image of P under the same translation?

4

P'

A

B C

O

P

Q

Diagram 6

-4 -2 0 2 4

4

4

2

-2

x

A B

C

D M

y

Diagram 7

4

S'

S

B D

A

C

P

Diagram 8

0 2 4 6 8

4

6

4

2

x

8

P

Q

Diagram 5

y


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9. Diagram 9 shows points plotted on a

Cartesian plane. Triangle P`Q`R` is theimage of triangle PQR under a rotation90o. Which of the point A, B, C and D

is the centre of rotation.

10. Diagram 10 below is drawn on aCartesian plane. State the coordinatesof the image of N under a rotation 90o

clockwise about (-2,0)

Diagram 10

A. ( 3, -4) B. (0,-3)

C. (-3, 0) D. (-4, 3)

11. The point A (-5, 7) is the image of point

A under a translation

6

8. Find the

coordinates of point A.

A. (3,1) B. (-3,-1)

C. (1,3) D. (-13,13)

12. The Diagram 11 below is drawn on a

Cartesian plane. State the coordinates ofThe image of P under a rotation 90

o

anti-clockwise about (1,-1).

A. (0,2) B. (2,-4)

C. (2,0) D. (1,2)

13

In Diagram 12 pentagon F is the image of

the pentagon E under a rotation of 90o

anticlockwise about (2,2). Find the coordinatesimage of K under the same rotation.

A. (1, 4) B. (4, 1)

C. (3, 0) D. (0, 3)

-4 -2 0 2 4

4

4

2

-2

x

-4

y

N

C

A

B D

Q

P

R4

p'

Q'

R'

Diagram 9

-4 -2 0 2 4

4

4

2

-2

x

-4

y

P

Diagram 11

0 2 4 6 8

4

4

2

x

6

E

F

y

Diagram 12

K


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14

In the diagram above, P is the image

of P under a translation. Which of the

points A, B, C or D is wrongly placed?

15 The coordinates N(3,4) is the image

of M(-2,1) under a translation

A.

3

5B.

5

3

C.

3

5D.

3

5

16 In Diagram 13, G is the image of H

under a translation

k

h.

The distance of GH is 13 units.

Translation

k

his

A.

13

5B.

3

5

C.

12

5D.

5

12

17 In the diagram above, R is the image ofT under a rotation of 90o. State the centre

and direction of the rotation.A.(4 , 0) clockwise

B. (4 , 0) anticlockwise

C.(4 , 4) clockwiseD.(4 , 4) anticlockwise

18

In diagram above,line PQ is the image of

line RS under a reflection. The axis of

reflection is

A. x = 2 B. x -axis

C. y -axis D y = 2

T

R

x

y

8

6

4

2

0

4

A

B

C

D

P

P'

-4 -2 0 2 4

4

4

2

-2

x

-4

Q

R

P

S

x

y

G(5,3)

H

O


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19

The above diagram shows seven pointsmarked on the same square grid. P is the

image of Q under a reflection. Which of thepoints A,B,C and D is the image of Sunder the same reflection?

20. The diagram above shows a triangle LMN.

Given that P is a reflection through a line

y = x . The coordinates of the image of Munder transformation P is

A. (3,2) B. (2,3)

C. (4,3) D. (1,3)

M

N

xO 2 4

2

4

L

P

Q

C

SD

B

A

y


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Transformation III 18

2.6 Past Year SPMQuestions

1. SPM Nov2003.

Diagram below shows five triangles drawn on a square grid.

Considering the four triangles, A, B, C and D, which of these is the image ofHunder a rotation

of 180o about the centre O.

2. SPM Nov 2003Diagram below shows seven points on a square grid. Q is the image of P under a reflection.

The axis of reflection is the straight line that joins H and

A K B LC M D N

3. SPM Nov 2003

Diagram shows that N is the image of M under a translationh

k

. The distance of MN is 5 units.

The translation is

A.

3

5

B.5

3

C.4

3

D.3

4

M4

P. L

K

N

Q

H

4

O

A

B

C D

H

x

y

M(-3,6)

N

O


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4. SPM July 2004

In the Diagram, O is the origin of a Cartesian plane. Point N is the image of point M(12, 7)

under a translationh

k

. If the distance of MN is 13 units, thenh

k

is

A.7

12

B.12

5

C.12

5

D.12

7

5. SPM July 2004

Diagram shows points plotted on a Cartesian

plane.

6. SPM Nov 2004

Diagram below shows two squares, R and S, drawn on a square grid.

S is the image of R under an enlargement. Which of the point, A, B, C or D is the centre of theenlargement?

R

S

D

A B

C

0 2 4 6 8 10A

4

C

D

B

H

2

4

6

x

y

x

y

M

N

O

Which of the point, A, B, C and D isthe image of H under a reflection

about the straight line y =2

1x?


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7. SPM Nov 2004Diagram 4 below shows points plotted on a Cartesian plane.

Which of the point, A, B, C and D is the image of K under a clockwise rotation of 90o

about

the centre (3, -1) ?

8. SPM July 2005

Diagram 3 is drawn on square grids. Quadrilateral KPQR is the image of quadrilateralKLMN under an enlargement.

Which of the following gives the correct centre and scale factor of the enlargement?

Centre Scale factor

A. K 2

B K 3C M 2D M 3

y

-4 -2 0 2 4 64

-2

x

2

A

C D

B

K

Diagram 4

R

Q P

K

M L

N


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9. SPM July 2005Diagram 4 shows five points on a Cartesian plane.

Points P is the image of point Q under the translation

2

3.

Which of the point, A, B, C, and D ,represents point Q?

10. SPM Nov 2005

Diagram below shows five triangles drawn on square grids.

Which of the triangle A, B.C and D is the image of triangle P under an enlargement withscale factor 2?

4

P

A

B

CD

Diagram 5

O 2 4 6 8 10 x

4

A

P

CB

2

4

6

8

10

D

y


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11. SPM Nov 2005Diagram below shows two triangles, R and S, drawn on square grids.

S is the image ofR under a clockwise of 90o. Which of the point, A, B,

C or D, is the centre of the rotation?

12. SPM Jun 2006

Diagram shows five quadrilaterals drawn on a Cartesian plane.

Which of the quadrilaterals, A, B, C or D, is the image of M under a clockwise rotation of 90o

about the centre (1, 0) ?

13. SPM Jun 2006

Diagram shows a triangle KLM and a shaded triangle, drawn on square grids.

4

A

B

C

D

R

S

Diagram 6

OAB

C

D

M2

4 y

x

42

-2

-2

L

K

A

B

C

D

MTriangle KLM is the image of the shadedtriangle under an enlargement.

Which of the points A, B, C or D, is thecentre of the enlargement?


11/17


14. SPM Nov 2006

Diagram shows five triangles drawn on square grids.

Which of the triangles, A, B, C or D, is not an image of triangle P under a rotation?

15. SPM Nov 2006

In Diagram, the square UVWX is the image of the square STUR under an enlargement.

The centre of the enlargement and its scale factor are

Centre of Enlargement Scale Factor

A P 1

3

B P 3

C U1

3

D U 3


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16. SPM Jun 2007,Q10

Diagram 4 shows five points on a Cartesian plane.

Diagram 4

Which of the points A, B, C orD is the image of point H under a clockwise rotation of 90o

about the centre (1, 1)?

17. SPM Jun 2007,Q11

Diagram 5 shows five hexagons on a Cartesian plane.

Which of the hexagons, A, B, C or D, is the image of the hexagon P under the translation2

3

?

A

B

C

D H

A

BC

D

P

Diagram 5


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18. SPM Jun 2007,Q12

Diagram 6 shows two quadrilaterals, TVWZ and PQRS, drawn on a Cartesian plane.Quadrilateral TVWX is the image of quadrilateral PQRS under an enlargement.

Diagram 6

The coordinates of the centre of enlargement is

A (3, 7)

B (4, 8)

C (5, 9)

D (6, 10)

19. SPM Nov 2007,Q9

Diagram 4 shows four quadrilaterals, W, X, Y and Z, drawn on square grids.

All the quadrilaterals are rotated 90o about the centre O.Which of the following is the correct rotation?

P

Q

R

S

T

W

ZV

X

Y

Z

WO

Diagram 4


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Quadrilateral Direction of rotation Image

A W Clockwise Z

B X Anticlockwise Y

C Y Anticlockwise X

D Z Anticlockwise W

20. SPM Nov 2007,Q10

Diagram 5 shows two squares, PQRS and KLMN, drawn on square grids.

Diagram 5

PQRS is the image of KLMN under an enlargement with centre O.Find the scale factor of the enlargement.

A1

3

B1

2

C 2

D 3

P

Q

R

S

M

N

K

L

O


15/17


21. SPM Jun 2008,Q11

Diagram 6 shows two polygons, PQRST and UVWXY, drawn on square grids. UVWXY is the

image of PQRST under an enlargement.

Diagram 6

What are the centre and the scale factor of the enlargement?

Centre of Enlargement Scale Factor

A H 2

B H - 2

C K 2

D K - 2

22. SPM Nov 2008,Q9

In Diagram 4, pentagon N is the image of pentagon M under a clockwise rotation of 90o.

Diagram 4

Which of the points A, B, C orD, is the centre of the rotation?

P Q

RS

T

UV

W X

Y

H

K

A B C

DN

M


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23. SPM Nov 2008,Q10

Diagram 5 shows five quadrilaterals P, A, B, C and D, drawn on square grids.

Diagram 5

Which of the quadrilaterals A, B, C orD is the image of quadrilateral P under an enlargement?

A

B

C

D

P


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T f ti III 29

ANSWERS

Chapter 2 Transformations I, II

No Answer No Answer

1 A 11 A2 B 12 A

3 B 13 A

4 C 14 A

5 C 15 A

6 A 16 C

7 C 17 B

8 B 18 A

9 B 19 B

10 C 20 A

SPM past Year question

Year No Key No Key No Key

Nov 2003 1 C 2 B 3 C

Jun 2004 4 A 5 B

Nov 2004 6 D 7 C

Jun 2005 8 B 9 A

Nov 2005 10 A 11 D

Jun 2006 12 A 13 A

Nov 2006 14 D 15 B

Jun 2007 16 B 17 B 18 C

Nov 2007 19 C 20 D

Jun 2008 21 A Nov 2008 22 D 23 C

chapter 2 i transformation i,ii enhance(2)

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