SPM Mathematics Trial 2021 (Kelantan), Paper 2 (Question 15)

Question 15:
Diagram 5 shows two trapeziums, PQRS and P’Q’R’S’. P’Q’R’S’ is the image of PQRS under combine transformation AB.
Diagram 5

(a) Describe transformation A and transformation B. [6 marks]
(b) Given the area of the trapezium PQRS is 20 units², calculate the area of the trapezium P’Q’R’S’ in units²? [3 marks]


Solution:
(a)
(i) Transformation B is rotation 180^o at centre (1, 0).

(ii) Transformation A is enlargement with scale factor 2 at centre (3, -2).

$\text{Scale factor, }k=\frac{P‘S‘}{PS}=\frac{4}{2}=2$


(b)
Area P’Q’R’S’ = (Scale factor) ² × Area PQRS
= 2² × 20
= 80 units²