chapter 12 ii transformations iii (2) enrich

8/3/2019 Chapter 12 II Transformations III (2) ENRICH

1/13

Enrichment

12.5 Past Year SPM Questions

November 2003

1. Diagram 7 shows trapeziums ABCD, ABEF, GHJK and LMNP on a Cartesianplane.

(a) Transformation Ris a reflection about the line y = 3. Transformation T is the

translation

4

2

.

State the coordinates of the image of pointHunder the following transformations:

(i) RT,

(ii) TR.[4 marks]

(b) ABEFis the image ofABCD under transformation V and GHJKis the image ofABEFunder transformation W.Describe in full

(i) transformation V,

(ii) a single transformation which is equivalent to transformation WV.

[5 marks]

(c) LMNPis the image ofABCD under an enlargement.

(i) State the coordinates of the centre of the enlargement.(ii) Given that the area ofLMNPis 325.8 units2, calculate the area ofABCD.

[3 marks]

12 Transformations 14

4

2

6

8

2 4-4 -2 0 6-6 8 10

A

BC

D

E F

G

H

JK

L

MN

P

DIAGRAM 7

y

x


2/13

Enrichment

July 2004

2(a) Transformation U is a translation

23

.

Transformation V is a reflection in the straight line x = 2.

State the coordinates of the image of point (3,4) under the following transformations:

(i) U,(ii) UV.

[3 marks]

(b) Diagram 6 shows three trapeziumsABCD, MNCHandEFGHon a Cartesian plane.

MNCHis the image ofEFGHunder transformation W andABCD is the image ofMNCH

under transformation Z.

(i) Describe in full(a) the transformation W,

(b) the transformation Z.

(ii) Given that the trapezium MNCHrepresents a region of area 22 m2, calculate the area

of the region represented by the hexagon ABNMHD.

[9 marks]


4

2

6

8

2 4-4 -2 0 6-6 8

10

x

y

DIAGRAM 6

A B

CD

EF

GH

M N


3/13

Enrichment

November 2004

3. Diagram 6 shows quadrilaterals,ABCD,PQRSandKLRM, drawn on a Cartesian plane.

a) Transformation T is a translation

24

.

Transformation V is a reflection in the line y = 1.

State the coordinates of the image of point A under each of the following

transformations:(i) Translation T.

(ii) Combined transformations VT.

[3 marks]b)

(i) KLRMis the image ofABCD under the combined transformations WU.Describe in full, the transformation U and the transformation W.

(ii) Given that the shaded regionKLQPSMrepresents a region of area 120m2, calculate

the area, in m2, of the region represented byPQRS.

[9 marks]

July 2005

4 (a) Diagram 7 in the answer space shows pointA, pointJand straight lineKLdrawn on a Cartesian plane.

Transformation T is a translation

14

.

Transformation P is a reflection in the straight line x = -2.

Transformation Ris a rotation of 90 clockwise about the centreA.

(i) On Diagram 7 in the answer space, draw the image of straight lineKL under

translation T.


DIAGRAM 6

4

2

6

8

2 4-4 -2 0 6 8 x

y

10 12

A

B

C

D

L

M

K

Q

R

S

P


4/13

Enrichment

(ii) State the coordinates of the image of pointJunder the following

transformation:

(a) P,(b) RT.

[4 marks]

(b) Diagram 8 shows three quadrilaterals,ABCD,EFGHandPQRS, drawn on aCartesian plane.

EFGHis the image ofABCD under transformation V.PQRSis the image ofABCD under transformation W.

(i) Describe in full the transformation:

(a) V,(b) W.

(ii) Given that the quadrilateralABCD represents a region of area 32.8m2,

calculate the area of the region represented by the quadrilateralPQRS.[8 marks]


DIAGRAM 8

2

-2

4

6

2 4-4 -2 0 6-6x

y

-4

K

L

J

A

2

4

6

2 4-4 -2 0 6-6x

y

-2

E

F

G

HP R

S

A

B

C

D

Q


5/13

Enrichment

November 2005

5(a) Diagram 6 shows two points, MandN, on a Cartesian plane.

Transformation T is a translation

13

.

Transformation Ris an anticlockwise rotation of 90 clockwise about the centre(0, 2).

(i) State the coordinates of the image of point Munder transformation R.(ii) State the coordinates of the image of pointNunder the following

transformation:

(a) T2,

(b) TR.[5 marks]

(b) Diagram 7 shows three quadrilaterals,ABCD,EFGHandPQRSon a Cartesian

plane.

EFGHis the image ofABCD under transformation V.PQRSis the image ofABCD under transformation W.

(ii) Describe in full the transformation:

(a) V,(b) W.

(iii) Given that the quadrilateralPQRSrepresents a region of area 45.6cm2,

calculate the area, in cm2, represented by the shaded region.

[7 marks]


DIAGRAM 62

-2

4

2 4-4 -2 0 6x

y

-4

M

N

DIAGRAM 7

4

2

6

2 4-4 -2 0 6 8x

y

C

B

A

D

E

F

G

H

P

Q

R

S


6/13

Enrichment

July 2006

6. Diagram 6 shows three quadrilaterals,ABCD, EFLKandEGHJ, drawn on a Cartesianplane.

(a) Transformation T is a translation

1

5

.

Transformation P is a reflection on the line y=4.

State the coordinates of the image of pointKunder each of the followingtransformations:

(i) Translation T,(ii) Combined transformations PT.

[3 marks]

(b) EGHJ isthe image ofABCD under the combined transformations WV.

(i) Describe in full the transformation:(a) V,

(b) W.

(ii) It is given that the quadrilateralABCD represents a region of area 21 m2.

Calculate the area, in m2, represented by the shaded region FGHJKL.

[9 marks]


DIAGRAM 6

0 2-6 -4 -2 4-8 6

4

2

6

8

10

x

y12

AB

C

D

E

F

G

H J

KL


7/13

Enrichment

November 2006

7. (a) Transformation T is a translation3

2

and transformation P is an anticlockwise

rotation of 90o about the centre (1,0).

State the coordinates of the image of point (5, 1) under each of the following

transformations:(i) Rotation P

(ii) Translation T,

(iii) Combined transformations T2.[4 marks]

(b) Diagram 6 shows three quadrilateralsABCD,EFGHandJKLM, drawn on a

Cartesian plane.

(i)JKLM isthe image ofABCD under the combined transformations VU.

Describe in full the transformation:

(a) U,(b) V.

(ii) It is given that the quadrilateralABCD represents a region of area 18 m2.Calculate the area, in m2, of the region represented by the shaded region .

[8 marks]


0 2-6 -4 -2 4 6

DIAGRAM 6

4

2

6

8

x

y

8

A

BC

D

J

E

F G

H

KL

M

642O-2-4


8/13

Enrichment

8. SPM Jun 2007

Diagram 7 shows quadrilaterals ABCD and JKLM drawn on a Cartesian plane.

a) Transformation T is a translation3

2

. Transformation P is a reflection in the straight

line 3y = .

State the coordinates of the image of point K under the following transformations:(i) T2

(ii) TP

[4 marks]

b) (i) JKLM is the image of ABCD under the combined transformation HG.Describe in full, the transformation:

(b) G

(c) H

(ii) Given that JKLM represents a region of area 160 m2, calculate the area, in m2, of

the region represented by ABCD.

[8 marks]


DIAGRAM 7

A

BC

D

J K

L

M

x

y


9/13

Enrichment

9. SPM Nov 2007, Q15

Diagram 8 shows quadrilaterals ABCD, EFGH and JKLM drawn on a Cartesian plane.

(a) Transformation Ris a rotation of 90o anticlockwise about the centre (0, 2).

Transformation P is a reflection in the straight line 2x = .

State the coordinates of the image of point A under each of the following

transformations:(i) R

(ii) RP

[4 marks]

(b) EFGH is the image of ABCD under the combined transformation MN.

Describe in full,

(i) the transformation M

(ii) the transformation N

[4 marks]

(c) JKLM is the image of EFGH under an enlargement at centre (3, 0).

(i) State the scale factor of the enlargement.

(ii) Given that EFGH represents a region of area 112 m2, calculate the area, in m2, ofthe region represented by JKLM.

[4 marks]


A B

C

D

EF

G

H

JK

L

M

DIAGRAM 8


10/13

Enrichment

10. SPM Jun 2008, Q13

Diagram 13 shows quadrilaterals ABCD, EFGH and PQRS drawn on a Cartesian plane.

(a) Transformation T is a translation3

1

.

Transformation U is a reflection in the line BF.

State the coordinates of the image of point E under each of the following combinedtransformations:

(i) T2

(ii) TU

[4 marks]

(b) EFGH is the image of ABCD under a combined transformation WV.Describe in full the transformation

(i) V

(ii) W

[4 marks]

(c) PQRS is the image of EFGH under the enlargement.(i) State the centre and the scale factor of the enlargement.(ii) It is given that ABCD represents a region of area 14.5 m2. Calculate the area, in

m2, of the region represented by PQRS.

[4 marks]


A

B

C

D

E

F

G

H P

Q

R

S

Diagram 13


11/13

Enrichment

11. SPM Nov 2008 Q13

(a) Transformation P is a reflection in the linex k= .Transformation Ris clockwise rotation of 90o about the centre (0, 4).

Transformation T is a translation5

3

.

(i) The point (8, 6) is the image of the point (- 4, 6) under the transformation P.State the value ofk.

(ii) Find the coordinates of the image of point (2, 8) under the following

combined transformations.a. T2

b. TR

[5 marks]

(b) Diagram 13 shows three pentagons, ABCDE, FGHIJ and KLMNJ, drawn on a

Cartesian plane.

Diagram 13

(i) KLMNJ is the image of ABCDE under a combined transformation VU.Describe in full, the transformation

(a) U

(b) V

(ii) It is given that the pentagon KLMNJ represents a region of area 42.5 m2.

Calculate the area, in m2, of the region represented by the coloured region.

[7 marks]


A

BC

D

E

F

G H

I

J

N

ML

K


12/13

Enrichment

ANSWERS

SPM Past Years Questions

1. SPM 2003

(a) (i) (7, 0) (ii) (7, 8)

(b) (i) (a) V = Reflection at the line AB

(b) WV = Rotation 90o anti-clockwise about point (6, 5)

(c) (i) (6, 2) (ii) 36.2

2. SPM Jun 2004

(a) (i) (6, 2) (ii) (4, 2)

(b) (i) (a) W = Rotation 180o clockwise about H.

(b) Z = Enlargement with scale factor 3 at point C.

(ii) 176

3. SPM Nov 2004

(a) (i) (2, 4) (ii) (2, -2)

(b) (i) (a) U = Rotation 90o clockwise about point (0,1).(b) W = Enlargement with scale factor 3 at point R.

(ii) 15

4. SPM Jun 2005

(a) (i) (-5, 4) (ii) (1, -3)

(b) (i) (a) V = Rotation 90o clockwise about point (-3, 5).

(b) Z = Enlargement with scale factor 2 at point (4, 7) .

(ii) 131.2

5. SPM Nov 2005

(a) (i) (3, 4) (ii) (a) (2, 1) (b) (2, -3)

(b) (i) (a) W = Reflection at the line x = 3.

(b) Z = Enlargement with scale factor 2 at point (1, 2).

(ii) 34.2

6. SPM Jun 2006

(a) (i) (-2, 7) (ii) (-2, 1)

(b) (i) (a) V = Rotation 90o clockwise about point (-1, 0).(b) W = Enlargement with scale factor 2 at point E.

(ii) 63

7. SPM Nov 2006

(a) (i) (0, 4) (ii) (2, 3) (iii) (-1, 5)

(b) (i) (a) V = Reflection at the line x = -1(b) W = Enlargement with scale factor 3 at point (2, 4).

(ii) 144



13/13

Enrichment

8. SPM Jun 2007

(a) (i) (3, 9) (ii) (6, 3)

(b) (i) (a) G = Rotation 90o clockwise, about centre (2, 6)

(b) H = Enlargement with scale factor 2 at point J(1, 5)(ii) 40

9. SPM Nov 2007

(a) (i) (-3, 5) (ii) (-3, 3)

(b) (i) (a) M = Enlargement with scale factor 2 at centre (3, 0)

(b) N = Rotation 180o, about centre (2, 4)

(c) (i)1

2(ii) 28 m2

10. SPM Jun 2008

(a) (i) (8, 3) (ii) (4, 5)

(b) (i) (a) V = Reflection in the line y = 4(b) W = Reflection in the line x = 0 (y-axis)

(c) (i) centre (-1, 5) with scale factor 2

(ii) 58 m2

11. SPM Nov 2008

(a) (i) k = 2 (ii) (a) (12, 2) (b) (9, -1)

(b) (i) (a) U = Reflection in the line x = 1

(b) V = Enlargement at point J (8, 1) with scale factor1

2(ii) Area of FGHIJ = 42.5 x 22 = 170

Area of coloured area = 170 42.5 = 127.5 m2.


chapter 12 ii transformations iii (2) enrich

Documents