Question 9:
(a) Diagram 8.1 shows point K ( 3, 2 ) marked on a Cartesian plane.
Diagram 8.1
The transformation T is a translation
The transformation R is a reflection in the line y = 3.
State the coordinates of the image of point K under each of the following transformations.
(i) T
(ii) TR [3 marks]
Diagram 8.2
(i) Trapezium PTUV is the image of trapezium ABCD under the combined transformation VW. Describe in full, the transformation W and the transformation V. [ 6 marks]
(ii) Given that the area of trapezium ABCD is 14 cm2, calculate the area, in cm2, of the shaded region. [3 marks]
Solution:
(a)(i) (3, 2) → T → (1, 5)
(a)(ii) (3, 2) → R → (3, 4) → T → (1, 7)
(b)(i)
W : Rotation, 90o clockwise at centre (0 , −1)
V: Enlargement, scale factor of 2, centre of enlargement at point P (2 , 1)
(ii)
Area of PTUV = (scale factor)2 × Area of object
= 22 × 14
= 56 cm2
Area of shaded region = 56 – 14 = 42 cm2