SPM Practice (Long Questions)

Question 8:
(a) Diagram 8.1 shows point A and point B marked on a Cartesian plane.

Diagram 8.1

Transformation R is a rotation of 90^o, clockwise about the centre B.

Transformation T is a translation $\left(\begin{array}{l}5\\ -2\end{array}\right)$

State the coordinates of the image of point A under each of the following transformations:
(i) RT,
(ii) R².

(b) Diagram 8.2 shows three trapeziums ABCD, PQRS and TUVS, drawn on a Cartesian plane.

Diagram 8.2

(i) Trapezium PQRS is the image of trapezium ABCD under the combined transformation MN.
Describe in full, the transformation:
(a) N,  
(b) M.

(ii) It is given that trapezium ABCD represents a region of area 30 m².
Calculate the area, in m², of the shaded region.


Solution:
(a)


(i) A (–1, 6) → T → (4, 4 ) → R → (3, 1)
(ii) A (–1, 6) → R → (5, 6) → R → (5, 0)

(b)(i)(a)
N is a reflection in the line y = 4.

(b)(ii)(b)
M is enlargement of scale factor 2 with centre S (1, 5).

(b)(ii)
Area of PQRS = (scale factor)² x Area of object ABCD
 = 2² x 30
 = 120 m²

Therefore,
Area of shaded region
= Area PQRS – area ABCD
= 120 – 30
= 90 m²