MODUL 11 SKIM TIUSYEN FELDA (STF) MATEMATIK SPM ENRICHMENT TOPIC : TRANSFORMATIONS TIME : 2 HOUR
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1 MODUL 11 SKIM TIUSYEN FELDA (STF) MATEMATIK SPM ENRICHMENT TOPIC : TRANSFORMATIONS TIME : HOUR 1. (a) Diagram 1 shows two points, M and N, on a Cartesian plane. N M - - DIAGRAM 1 3 Transformation Y is a translation. 3 Transformation P is a reflection in the -ais. (i) State the coordinates of the image of point N under transformation Y. State the coordinates of image of point M under the following transformation: (a) Y (b) YP (a) (i) (a) (b)
2 (b) Diagram shows three trapezium ABCD, EFGH and PQRS on a Cartesian plane. R S F G P Q D E C H A B O 8 10 DIAGRAM 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 [ marks] (b) (i) (a) Calculate the area of trapezium EFGH, if the area of trapezium ABCD is 5 unit. (b)
3 . (a) Diagram 3 shows the point K on a Cartesian plane. K DIAGRAM 3 The transformation R represents a 90 0 anticlockwise rotation about the center (3, ). The transformation T represents a translation. State the coordinates 3 of the image of the point K under the following transformations. (i) R RT (a) (i)
4 (b) Diagram 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. B C A D - - O E F - H G - K J DIAGRAM (i) Describe completel the transformation, (a) U, (b) V. [ marks] Given that the shaded area is 10 unit, find the area of ABCD. (b) (i) (a) (b)
5 3. (a) Diagram 5 shows the point K on a Cartesian plane. 10 F DIAGRAM 5 5 Transformation S is a translation. Transformation T is a reflection in the = 9. (i) State the coordinates of the image of point F under transformation S. State the coordinates of image of point F under transformation TS. (a) (i)
6 (b) Diagram shows three triangle PQR, ACG and EFG on a Cartesian plane. 10 F 8 A P G C E O Q R DIAGRAM 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 Given that the area of triangle EFG represents a region of area 7 unit. Calculate the area, in unit, of the region represented b triangle PQR. [ marks] [ (b) (i) (a) (b)
7 . (a) Diagram 7 shows the point M on a Cartesian plane M O DIAGRAM 7 Transformation P is a reflection in the line = -3. Transformation R is a rotation of 90 o clockwise about the origin. State the coordinates of the image of point M under the following transformation: (i) P RP (a) (i)
8 (b) Diagram 8 shows three trapezium ABCD, RSTU and WSYX on a Cartesian plane. 10 W R S 8 U T A B X Y D C O DIAGRAM 8 WSYX is the image of ABCD under combined transformation UV. (i) Describe in full transformation : (a) U (b) V [5 marks] Given that the area of shaded region WXYTUR represents a region of area 150 cm. Calculate the area, in cm, of the region represented b RSTU. [ marks] (b) (i) (a) (b)
9 5. (a) Transformation R is a 90 clockwise rotation at centre (, ). Transformation T is a translation. 3 State the coordinate of the image for coordinate (, ) under the following transformations: (i) R. TR. [ marks] (a) (i) (b) Diagram 9 shows quadrilateral, ABCD, PQRS and EFGH, drawn on a Cartesian plane. H G S R C D P Q B A O F 8 - E - 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 (a)transformation S (b)transformation Q [5 marks] Given the area of ABCD is unit, calculate the area of shaded region. (b) (i) (a) (b)
11 JAWPAN MODUL11 TOPIC : TRANSFORMATIONS 1 (a) (i) (0, -1) 1 (a) (-3, -) 1 (b) (-1, -) 1 (b)(i)(a) M is a rotation of 90 o clockwise about point (1,3) 3 (b) N is an enlargement with centre at (,0) and a scale factor of 3 Area EFGH = k (Area ABCD) = (5) = 100 unit 3 (a)(i) (, -) 1 (1, 0) (b)(i)(a) U is a rotation of 90 o clockwise about the point (1, 1) 3 (b) V is an enlargement with centre at (, 0) and scale factor of 3 Area OFJK = k (Area ABCD) 10 + Area ABCD = (Area ABCD) Area ABCD = 0 unit 3 3 (a)(i) (1, 7) 1 (, 7) (b)(i)(a) V is a rotation of 90 o clockwise about point (7, 0) 3 (b) W is an enlargement with centre at (7, 3) and scale factor of 3 3 Area EFG = k (Area PQR) 7 = 3 (Area PQR) Area PQR = 8 unit 3 (a)(i) (-3, ) 1 (, 11) (b)(i)(a) 8 1 U is a translation 3 (b) V is an enlargement with centre at (-3, 8) and scale factor of. 3 Area WXYS = k (Area RSTU) RSTU = (Area RSTU) Area RSTU = 50 cm 5 (a)(i) (-3, 0) (, ) (b)(i)(a) S is a reflection in the line =1 Q is an enlargement with centre at (-11, ) and scale factor of. 3 Area ABCD + Area of shaded region= k (Area ABCD) + Area of shaded region = () Area of shaded region = (5 ) cm Area of the shaded region = 19 cm 3
12
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