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Module 11 Tansformation

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This document provides a series of math word problems involving transformations. It includes: 1) Five sections with multiple parts assessing skills with translations, reflections, rotations, and enlargements/reductions. Problems include finding coordinates of transformed points and describing transformations. 2) Diagrams of figures on Cartesian planes along with their transformed images under different combinations of transformations. 3) Calculating areas of transformed figures when given the area of the original figure. The document assesses a wide range of skills with geometric transformations, providing practice applying concepts of translations, reflections, rotations, and scale changes to specific word problems and diagrams.

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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 :

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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)

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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

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PPR Maths nbk

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Module 11 Tansformation

  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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