SPM Practice (Long Questions)

Question 7:
Diagram shows the point J(1, 2) and quadrilaterals ABCD and EFGH, drawn on a Cartesian plane.




(a) Transformation U is a rotation of 90^o, clockwise about the centre O.
Transformation T is a translation $\left(\begin{array}{l}\text{2}\\ 3\end{array}\right)$  
Transformation R is a reflection at the line x = 3.

State the coordinates of the image of point J under each of the following transformations:
(i) RU,
(ii) TR.

(b) EFGH is the image of ABCD under the combined transformation MN.
Describe in full, the transformation:
(i) N,   
(ii) M.

(c) It is given that quadrilateral ABCD represents a region of area 18 m².
Calculate the area, in m², of the shaded region.


Solution:




(a)
(i) J (1, 2) → U → (2, –1 ) → R → (4, –1)
(ii) J (1, 2) → R → (5, 2) → T → (7, 5)

(b)(i)
N is a reflection in the line x = 6.

(b)(ii)
M is enlargement of scale factor 3 with centre (8, 7).

(c)
Area EFGH = (scale factor)² x Area of object ABCD
 = 3² x 18
 = 162 m²

Therefore,
Area of shaded region
= Area of EFGH – Area of ABCD
= 162 – 18
= 144 m²