SPM Practice (Long Questions)

Question 6:
(a) Diagram below shows point M marked on a Cartesian plane.

Transformation T is a translation $\left(\begin{array}{l}\text{2}\\ 3\end{array}\right)$ and transformation R is an anticlockwise rotation of 90^o about the centre O.
State the coordinates of the image of point M under each of the following transformations:
(i) RT,
(ii) TR,

(b) Diagram below shows two hexagons, ABCDEF and JKLANO, drawn on square grids.



(i) JKLANO is the image of ABCDEF under the combined transformation VW.
Describe in full the transformation:
(a) W   (b) V

(ii) It is given that quadrilateral ABCDEF represents a region of area 45 m².
Calculate the area, in m², of the region represented by the shaded region.


Solution:
(a)

(b)



(i)(a)
V: A reflection in the line EC.

(i)(b)
$\begin{array}{l}\text{Scale factor}=\frac{KL}{BC}=\frac{6}{2}=3\\ \text{W: An enlargement of scale factor 3 at centre }J\text{.}\end{array}$

(ii)
Area of JKLANO
= 3² x area of ABCDEF
= 9 x 45
= 405 m²

Area of the coloured region
= area of JKLANO – area of ABCDEF
= 405 – 45
= 360 m²