Transformation III, Long Questions (Question 1)

Further Practice:
Transformation III, Long Questions (Question 1)

Question 1:
(a) Transformation is a translation $\left(\begin{array}{l}-4\\ \text{}2\end{array}\right)$ 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,