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SULIT NAMA: _______________________________________________ TINGKATAN: ______________ Lekat logo sekolah di sini TOPICAL TEST 3: TRANSFORMATION III PAPER 1 1 Diagram 1 shows five quadrilaterals If the area of the shaded region is image of point (–3, 3) under the are drawn on a Cartesian plane. 240 cm2, calculate the area, in cm2, combined transformation VU are of trapezium PQRS. A (3, 10) C (4, 10) A 30 C 80 B (3, 9) D (2, 7) B 60 D 90 8 Diagram 7 shows five congruent 5 Diagram 5 shows a point P is plotted trapeziums are drawn on a Cartesian on a Cartesian plane. plane. Diagram 1 Which of the quadrilaterals, A, B, C and D is the image of M under a clockwise rotation of 90° about centre (1, 0)? Diagram 7 Diagram 5 Transformation P is a clockwise 2 Diagram 2 shows five triangles are Transformation M is a reflection in rotation of 90° about the centre (1, drawn on square grids. the line y = x. Transformation N is a 0). Transformation Q is a reflection clockwise rotation of 90° about the in the line x = 4. Which of the centre (4, 2). Find the coordinates of shapes, A, B, C and D is the image the image of point P under the of shape X under the combined combined transformation NM. transformation QP? A (5, 1) B (3, 2) 9 Diagram 8 shows a kite. C (4, 1) Diagram 2 D (5, 2) Which of the triangles, A, B, C and 6 Diagram 6 shows a point S is plotted D, is the image of triangle P under a on a Cartesian plane. rotation of 180° about the centre O? 3 Diagram 3 shows two trapeziums P and Q. Q is the image of P under an enlargement. Diagram 8 Rajah 8 Transformation P is a clockwise rotation of 90° about point E. Transformation Q is an enlargement Diagram 6 with centre K and with a scale factor Transformation Q is a reflection in the of 2. Find the coordinates of the Diagram 3 line x = 3. Transformation R is a image of point H under the Which of the points, A, B, C and D combined transformation QP. translation 3 . Find the coordinates A (5, 3) C (6, 3) is the centre of enlargement? 4 B (5, 2) D (6, 2) of the image of point S under the 4 In Diagram 4, trapezium PTUV is combined transformation RQ. the image of trapezium PQRS under 10 Diagram 9 shows a triangle X with a A (5, 1) C (0, 2) point K. an enlargement. B (8, 0) D (5, 2) 7 Transformation U is a translation 4 . 1 Transformation V is an enlargement about the centre (0, 1) and a scale factor of 3. The coordinates of the Diagram 4 © Navision (M) Sdn. Bhd. (690640-P) 9 SULIT Given Q = Translation 1 , B (–2, 2) 2 C (2, –2) D (–2, –2) R = Translation 2 , 1 19 Given J = Rotation of 180° about a S = Clockwise rotation of 90° about (2, 2), point (4, 0), T = Rotation 180° about the K = Reflection in the line point (3, 3). y = –x. The combined transformation that The image of point (3, 0) under the Diagram 9 maps M onto N is combined transformation JK is Given R = Rotation of 180° about A QS C TQ A (8, 3) point (2, 2), B RS D QT B (–6, –3) S = Enlargement with centre 14 P is a reflection in the line y = –2 C (8, 4) (2, 2) and a scale factor of D (–6, –4) and Q is a translation 2 . Find the 2. 5 The coordinates of K under the 20 Transformation F is a reflection in coordinates of the image of the line y = 3. combined transformation SR are M(–2, 1) under the combined A (–4, –1) C (–3, –1) Transformation E is a reflection in transformation PQ. the line y = x. B (0, –2) D (–3, –2) A (0, –11) C (–10, 0) State the coordinates of image of B (–11, 0) D (0, –10) point R(3, 1) under the combined 11 In Diagram 10, N is the image of M under a combined transformation JK. transformation FE. 15 M is a translation 3 and N is A (3, 5) C (1, 3) 4 B (3, 1) D (5, 3) translation 5 . The image of point 3 21 Given R = Reflection in the line y = x, S = Rotation of 180° about (8, 2) under the combined transformation MN is the A (0, –1) origin, C (0, 1) B (0, 2) D (1, 0) T = Translation 0 , 2 Diagram 10 Rajah 10 16 In Diagram 12, Q is the image of P U = Enlargement at the origin K is a translation 4 and J is reflection in the line 3 under a translation x . y with a scale factor of 2. Q(2, 6) is the image of P(6, 4) under the combined transformation of A y = 2x A TR C TS B y=x B RT D SU C y= 1x 22 Diagram 13 is drawn on square 2 D y=0 grids. J', the image of J under a transformation, is mapped onto J" 12 Transformation T is the translation under another transformation. 2 and transformation S is a Diagram 12 1 Given the distance PQ is 10 units, reflection in the line y = x. The the translation is coordinates of the image of point A 2 C 8 (10, 2) under the combined 6 6 transformation ST are A (3, 7) C (3, 8) B 6 D 6 2 B (4, 7) D (8, 3) 8 Diagram 13 13 Diagram 11 shows two squares, M and 17 Given U = Reflection in the line y = x, Which of the points, A, B, C and D N. V = Clockwise rotation of 90° is the image of point M under of about (2, 1). same combined transformation? Find the coordinates of image of point (4, 2) under the combined transfor- 23 Diagram 14 shows a polygon K is mation VU. drawn on a Cartesian plane. A (–1, –5) Transformation X is a reflection in the B (1, 5) line y = 1. Transformation Y is a C (4, 1) reflection in the line x = 5. Polygon K D (5, 1) undergoes a combined transformation YX. 18 R is a reflection in the line Diagram 11 y = x. The image of (2, 2) under the combined transformation R2 is A (2, 2) © Navision (M) Sdn. Bhd. (690640-P) 10 SULIT Transformation P is a translation 2 3 . Transformation Q is a 25 In Diagram 16, K is the image of J under a combined transformation. clockwise rotation of 90° about the centre (0, 7). Diagram 14 A single transformation which is equivalent to YX is Diagram 16 Which of the following is not the A a reflection in the line y = x. possible combined transformation? Diagram 15 Rajah 15 B a rotation of 180° about the A Enlargement followed by rotation Which of the point, A, B, C and D is centre (5, 1). B Enlargement followed by the image of point E under the C an anticlockwise rotation of 90° reflection combined transformation QP? about the centre (4, 4). C Reflection followed by D a reflection in the line y = 4. enlargement D Translation followed by 24 Diagram 15 shows five points are enlargement drawn on a Cartesian plane. PAPER 2 1 Transformation U is an anticlockwise rotation of 90° 2 Transformation U is a clockwise rotation of 90° about the about the centre (0, 3) and transformation V is a origin. Transformation V is a reflection in the line x = 3. translation 2 . 3 On Diagram 2, draw the image of the triangle CDE under the each of following combined transformations. (a) VU, On Diagram 1, draw the image of line PQ under the (b) UV. combined transformation VU. [4 marks] [2 marks] Diagram 1 Diagram 2 © Navision (M) Sdn. Bhd. (690640-P) 11 SULIT 3 Transformation G is a translation 3 . 2 6 Diagram 4 shows three trapeziums, A, B and C. Transformation H is an enlargement at the origin with a scale factor 2. State the coordinates of the image of point (1, –2) under each of the following combined transformations. (a) HG, (b) GH. [4 marks] Diagram 4 (a) Point P is the image of point Q under a reflection. State the coordinates of the image of point R under the 4 Transformation A is a reflection in the line y = –x. same reflection. Transformation B is a clockwise rotation of 90° about the [2 marks] centre (–2, 1). State the coordinates of the image of point (2, (b) B is the image of A under a transformation V. C is the 3) under each of the following combined transformations. image of B under a transformation W. Describe in full (a) AB, (c) BA, (e) A2, (i) V, [6 marks] (ii) W. [4 marks] (c) State the coordiantes of the image of point R under the following transformations. (i) VW, (ii) WV. [4 marks] 5 Diagram 3 shows point A drawn on a Cartesian plane. 7 Diagram 5 shows three quadrilaterals, ABCD, JKLM and JPQR on a Cartesian plane. Diagram 3 Rajah 3 Transformation T is a translation 4 . Transformation U is 2 a reflection in line y = x. Transformation V is a clockwise rotation of 90° about the centre (0, 1). Transformation S is a reflection in line y = –x. State the coordinates of the image of point A under following transformations. (a) TV, (b) ST, (c) TS, (d) UV, (e) TU, (f) US. Diagram 5 [12 marks] JPQR is the image of ABCD under the combined transformation VW. (a) Describe the full transformation (i) V, (ii) W. [4 marks] (b) Given T = reflection in the line y = 2, R = translation 3 . 2 State the coordinates image of S(4, 0) under following transformations. (i) TR, (ii) RT. [4 marks] © Navision (M) Sdn. Bhd. (690640-P) 12 SULIT 8 (a) Transformation M is a translation 2 . Transformation 3 10 Diagram 7 shows four triangles, P, Q, R and S. N is a reflection in the line y = 5. State the coordinates of image of point (1, 3) under the following transformations. (i) M, (ii) N, (iii) MN. [4 marks] (b) S(–4, 3) is the image of T under a translation 2 . Find 3 Diagram 7 the coordinates of point T. (a) Triangle Q is the image of triangle P under a rotation. [2 marks] State (c) U(4, 3) is the image of V(2, 4) under a combined (i) the coordinates of the centre of the rotation, transformation TF. Describe in full the transformation (ii) the angle of the rotation. (i) T, [2 marks] (ii) F. [4 marks] (b) Find the coordinates of the image of point F(2, 1) under a translation 3 followed by a reflection in the 1 line y = –1. [2 marks] (c) Triangle R is the image of triangle Q under a combined transformation WV. Describe in full the transformation. (i) V, (ii) W. [4 marks] 9 (a) Given R is an anticlockwise rotation 90° about the centre (2, 2), 11 Diagram 8 shows three points, P', Q and Q', on a Cartesian T is a translation 2 . plane. 4 State the coordinates of the image of point (1, 2) under each of the following transformations. (i) T, (ii) R, (iii) TR, (iv) RT. [6 marks] (b) In Diagram 6, triangle ABC is the image of triangle DEF under a combined transformation WV. Diagram 8 (a) State the values of h dan k, if point Q' is the image of point Q under a translation h . k [2 marks] (b) Find the coordinates point P, if P' is the coordinates Diagram 6 image of P under translation h . k [2 marks] Describe in full the transformation (c) Given A = reflection is the y-axis, (i) V, B = rotation of 90° clockwise about the centre (ii) W. [4 marks] (0, 0). Find the coordinates of the image of P under the combined transformation AB. [2 marks] © Navision (M) Sdn. Bhd. (690640-P) 13 SULIT 12 In Diagram 9, quadrilateral JKLM is the image of 14 Diagram 11 shows three trapeziums, ABCD, EFGH and quadrilateral EFGH under a transformation X whereas HPQR. quadrilateral PQRS is the image of quadrilateral JKLM under a transformation Y. Diagram 11 Diagram 9 (a) Given T = translation 2 , (a) Describe in full the transformations X and Y. 1 [4 marks] (b) By determining the image of EFGH under the combined V = reflection in the line y = 3, transformation YX, describe a single transformation W = reflection in the y-axis. which is equivalent to YX. (i) Find coordinates of the image of point A under [2 marks] transformation W. (ii) Find the coordinates of the image of point C under transformation V. (iii) Find the coordinates of the image of point D under the combined transformation TV. [4 marks] (b) HPQR is the image of quadrilateral EFGH under a transformation S. (i) Describe in full the transformation S. (ii) If the area of EFGH is 16 cm2, calculate the area of HPQR in cm2. 13 (a) Given L = reflection in the line y = x, [5 marks] M = translation 2 . 1 N = anticlockwise rotation of 90° about the centre (2, 1). Find the coordinates of the image of point (3, 2) under each of following transformations. (i) M2, (ii) ML, (iii) LN, (iv) MN. [8 marks] (b) On Diagram 10, draw the images of the rectangle ABCD under the following combined transformations. (i) MN, (ii) NM. [4 marks] 15 (a) Given H = reflection at the line y =2, G = translation 2 . 1 Find the coordinates of the image of point A(2, 4) under each of the following transformations. (i) H, (ii) HG, (iii) GH. [5 marks] (b) In Diagram 12, triangle ABC is the image of the Diagram 10 triangle PQR under a transformtion U. Triangle DEF is the image of ABC under a transformation V. Diagram 12 Rajah 12 © Navision (M) Sdn. Bhd. (690640-P) 14 SULIT (i) Describe in full the transformations U and V. (ii) It is given that triangle DEF represents a region of area 72 m2. Calculate the area, in m2, of the region represented by triangle PQR. [7 marks] Diagram 14 Pentagon AFGHJ is the image of pentagon ABCDE 16 (a) Given P = reflection in the x-axis, under a transformation V and pentagon AKLMN is the T = clockwise rotation of 90° about the centre image of pentagon AFGHJ under a transformation W. (–2, 1). (i) Describe in full the transformations V and W. State the coordinates of image of point (1, 1) under (ii) It is given that the area of shaded region is 150 each of the following transformations. cm2. Calculate the area of the pentagon ABCDE in (i) P2, cm2. (ii) PT, [7 marks] (iii) TP. [5 marks] (b) In Diagram 13, triangle DEC is image of triangle ABC under a transformation V. Triangle DFG is image of triangle DEC under a transformation W, 18 Diagram 15 shows four quadrilaterals, P, Q, R and S drawn on a Cartesian plane. Diagram 13 (i) Describe in full the transformations V and W. (ii) It is given that the area of triangle DEC is 12 m2. Calculate the area, in m2, of triangle DFG. [7 marks] 17 (a) Transformation T is a translation 2 . Diagram 15 3 (a) Transformation T is a translation 6 . Transformation Transformation R is a reflection in the line y = 3. 2 Transformation S is a clockwise rotation of 90° about M is an anticlockwise rotation of 90° about the point the centre (0, k). (2, 2). Find the coordinates of the image of point (3, 1) (i) The point (3, 1) is the image of the point (–3, 1) under each of the following transformations. under the transformation S. State the value of k. (i) T, (ii) TM. [6 marks] (ii) Find the coordinates of the image of point (4, 2) (b) Q is the image of P under a transformation V and R is under each of the following transformations. the image of Q under a transformation W. Describe in (a) T2, (b) RT. full, [5 marks] (i) the transformation V. (b) Diagram 14 shows three pentagons, ABCDE, AFGHJ (ii) a single transformation which is equivalent to the and AKLMN are drawn on a Cartesian plane. combined transformation WV. [5 marks] (c) It is given that quadrilateral S is the image of the quadrilateral P under an enlargement. (i) State the coordinates of the centre of enlargement. (ii) It is given that the area of quadrilateral S is 108 cm2. Calculate the area of quadrilateral R, in cm2. [3 marks] © Navision (M) Sdn. Bhd. (690640-P) 15 SULIT