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# Module 11 Tansformation

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### Module 11 Tansformation

1. 1. PPR Maths nbk MODUL 11 SKIM TIUSYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT” TOPIC : TRANSFORMATIONS TIME : 2 HOUR 1. (a) Diagram 1 shows two points, M and N, on a Cartesian plane. y 2 N x -4 -2 0 2 4 M -2 -4 DIAGRAM 1 ⎛ − 3⎞ Transformation Y is a translation ⎜ ⎜ ⎟. ⎟ ⎝ − 3⎠ Transformation P is a reflection in the x-axis. (i) State the coordinates of the image of point N under transformation Y. (ii) State the coordinates of image of point M under the following transformation: (a) Y2 (b) YP [3 marks] Answer: (a) (i) (ii) (a) (b)
2. 2. PPR Maths nbk (b) Diagram 2 shows three trapezium ABCD, EFGH and PQRS on a Cartesian plane. R 6 S F G P Q 4 E H D C 2 A B O 2 4 6 8 10 DIAGRAM 2 Trapezium ABCD is the image of trapezium PQRS under transformation M. Trapezium EFGH is the image of trapezium ABCD under transformation N. (i) Describe in full transformation : (a) M (b) N [6 marks] (ii) Calculate the area of trapezium EFGH, if the area of trapezium ABCD is 25 unit2. [3 marks] Answer: (b) (i) (a) (b) (ii)
3. 3. PPR Maths nbk 2. (a) Diagram 3 shows the point K on a Cartesian plane. y 4 2 K -4 -2 0 2 4 6 x -2 -4 DIAGRAM 3 The transformation R represents a 90 0 anticlockwise rotation about the center ⎛ 2⎞ (3, 2). The transformation T represents a translation ⎜ ⎟ . State the coordinates ⎜ ⎟ ⎝ 3⎠ of the image of the point K under the following transformations. (i) R (ii) RT [3 marks] Answer: (a) (i) (ii)
4. 4. PPR Maths nbk (b) Diagram 4 shows three quadrilateral EFGH, ABCD and OFJK on a Cartesian plane. EFGH is the image of ABCD under the transformation U and OFJK is the image of EFGH under the transformation V . y B 4 C 2 A D E F -4 -2 O 2 4 6 x -2 H G -4 K J DIAGRAM 4 (i) Describe completely the transformation, (a) U, (b) V. [6 marks] (ii) Given that the shaded area is 120 unit 2 , find the area of ABCD. [3 marks] Answer: (b) (i) (a) (b) (ii)
5. 5. PPR Maths nbk 3. (a) Diagram 5 shows the point K on a Cartesian plane. y 10 F 8 6 4 2 x 0 2 4 6 8 10 12 14 16 DIAGRAM 5 ⎛ 5 ⎞ Transformation S is a translation ⎜ ⎜ ⎟. ⎟ ⎝ − 2⎠ Transformation T is a reflection in the x = 9. (i) State the coordinates of the image of point F under transformation S. (ii) State the coordinates of image of point F under transformation TS. [3 marks] Answer: (a) (i) (ii)
6. 6. PPR Maths nbk (b) Diagram 6 shows three triangle PQR, ACG and EFG on a Cartesian plane. y 10 F 8 6 A 4 P G C E 2 Q R x O 2 4 6 8 10 12 14 16 DIAGRAM 2 Triangle ACG is the image of triangle PQR under transformation V. Trapezium EFG is the image of triangle ACG under transformation W. (i) Describe in full transformation : (a) V (b) W [3 marks] (ii) Given that the area of triangle EFG represents a region of area 72 unit2. Calculate the area, in unit2, of the region represented by triangle PQR. [6 marks] [ Answer: (b) (i) (a) (b) (ii)
7. 7. PPR Maths nbk 4. (a) Diagram 7 shows the point M on a Cartesian plane. y 10 8 M 6 4 2 x -12 -10 -8 -6 -4 -2 O 2 4 DIAGRAM 7 Transformation P is a reflection in the line x= -3. Transformation R is a rotation of 90o clockwise about the origin. State the coordinates of the image of point M under the following transformation: (i) P (ii) RP [3 marks] Answer: (a) (i) (ii)
8. 8. PPR Maths nbk (b) Diagram 8 shows three trapezium ABCD, RSTU and WSYX on a Cartesian plane. y 10 W R S 8 6 U A B T 4 X Y 2 D C x -12 -10 -8 -6 -4 -2 O 2 4 6 DIAGRAM 8 WSYX is the image of ABCD under combined transformation UV. (i) Describe in full transformation : (a) U (b) V [5 marks] (ii) Given that the area of shaded region WXYTUR represents a region of area 150 cm2. Calculate the area, in cm2, of the region represented by RSTU. [4 marks] Answer: (b) (i) (a) (b) (ii)
9. 9. PPR Maths nbk 5. (a) Transformation R is a 90° clockwise rotation at centre (2, 2). ⎛ 4 ⎞ Transformation T is a translation ⎜ ⎜ ⎟. ⎟ ⎝ − 3⎠ State the coordinate of the image for coordinate (6 , 4) under the following transformations: (i) R2. (ii) TR. [4 marks] Answer: (a) (i) (ii) (b) Diagram 9 shows quadrilateral , ABCD, PQRS and EFGH, drawn on a Cartesian plane. y H G 6 S R C D 4 2 P Q B A -12 -10 -8 -6 -4 -2 O 2 4 6 F 8 x -2 E -4 DIAGRAM 9 PQRS is the image of ABCD under transformation S and EFGH is the image of PQRS under transformation Q. (i) Describe in full transformation :
10. 10. PPR Maths nbk (a)Transformation S (b)Transformation Q [5 marks] 2 (ii) Given the area of ABCD is 64 unit , calculate the area of shaded region. [3 marks] Answer: (b) (i) (a) (b) (ii)
11. 11. PPR Maths nbk JAWPAN MODUL11 TOPIC : TRANSFORMATIONS 1 (a) (i) (0, -1) 1 (ii)(a) (-3, -4) 1 (b) (-1, -2) 1 (b)(i)(a) M is a rotation of 90o clockwise about point (1,3) 3 (b) N is an enlargement with centre at (2,0) and a scale factor of 2 3 (ii) Area EFGH = k2(Area ABCD) = 22(25) 3 = 100 unit2 2 (a)(i) (4, -2) 1 (ii) (1, 0) 2 (b)(i)(a) U is a rotation of 90o clockwise about the point (1, 1) 3 (b) V is an enlargement with centre at (4, 0) and scale factor of 2 3 (ii) Area OFJK = k2(Area ABCD) 120 + Area ABCD = 22(Area ABCD) 3 Area ABCD = 40 unit2 3 (a)(i) (12, 7) 1 (ii) (6, 7) 2 (b)(i)(a) V is a rotation of 90o clockwise about point (7, 0) 3 (b) W is an enlargement with centre at (7, 3) and scale factor of 3 3 (ii) Area EFG = k2(Area PQR) 72 = 32(Area PQR) 3 Area PQR = 8 unit2 4 (a)(i) (-3, 6) 1 (ii) (6, 11) 2 (b)(i)(a) ⎛ − 8⎞ 1 U is a translation ⎜ ⎜ ⎟ ⎟ ⎝ 3 ⎠ (b) V is an enlargement with centre at (-3, 8) and scale factor of 2. 3 (ii) Area WXYS = k2(Area RSTU) 150 + RSTU = 22(Area RSTU) 4 Area RSTU = 50 cm2 5 (a)(i) (-3, 0) 2 (ii) (4, 4) 2 (b)(i)(a) S is a reflection in the line x =1 2 Q is an enlargement with centre at (-11, 2) and scale factor of 2. 3 (ii) Area ABCD + Area of shaded region= k2(Area ABCD) 64 + Area of shaded region = 22(64) 3 Area of shaded region = (256 – 64) cm2 Area of the shaded region = 192 cm2
12. 12. PPR Maths nbk