3.3 Transformation III, SPM Paper 2 (Long Questions)


Further Practice:
Transformation III, Long Questions (Question 1)
 
Question 1:
(a) Transformation is a translation ( 4 2 ) and transformation P is an anticlockwise rotation of 90oabout the centre (1, 0).
State the coordinates of the image of point (5, 1) under each of the following transformation:
(i) Translation T,
(ii) Rotation P,
(iii) Combined transformation T2.

(b) Diagram below shows three quadrilaterals, ABCD, EFGH and JKLM, drawn on a Cartesian plane.


 
(i) JKLM is the image of ABCD under the combined transformation VW.
Describe in full the transformation:
(a) W   (b) V

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


(b)

(i)(a)
W: A reflection in the line x = –2
 
(i)(b)
V: An enlargement of scale factor 3 with centre (0, 4).
 
(b)(ii)
Area of EFGH = area of ABCD = 18 m2
Area of JKLM = (Scale factor)2 × Area of object
= 32 × area of EFGH
= 32 × 18
= 162 m2
Therefore,
Area of the shaded region
= Area of JKLM – area of EFGH
= 162 – 18
= 144 m2

Question 2:
(a) Diagram below shows point A and straight line y + x = 5 drawn on a Cartesian plane.


Transformation T is a translation (  5 2 )
Transformation R is a reflection at the line y + x = 5.
State the coordinates of the image of point A under each of the following transformations:
(i) Transformation T,
(ii) Combined transformation TR.

(b) Diagram below shows pentagons JKLMN, PQRST and PUVWX, drawn on a Cartesian plane.

(i) PUVWX is the image of JKLMN under the combined transformation CB.
Describe in full the transformation:
(a) B    (b) C

(ii) It is given that pentagon JKLMN represents a region of area 80 m2 .
Calculate the area, in m2 , of the region represented by the shaded region.

Solution:
(a)

(i) (3, 4) → T → (8, 2)
(ii) (3, 4) → R → (1, 2) → T → (6, 0)

(b)

(b)(i)(a)
B: A clockwise rotation of  90o about the centre (0, 2).

(b)(i)(b)
Scale factor= PU PQ = 6 4 = 3 2 C: An enlargement of scale factor  3 2  with centre P( 2,0 )

(b)(ii)
Area of PQRST = Area of JKLMN
= 80 m2

Area of PUVWX = ( 3 2 ) 2 ×area of PQRST = 9 4 ×80 =180  m 2  Area of the shaded region = area of PUVWXarea of PQRST    =18080    =100  m 2

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