Further Practice:
Transformation III, Long Questions (Question 1)
Question 1:
(a) Transformation T is a translation
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