5.5.3 Combined Transformation, SPM Paper (Long Questions)

Question 5:
(a) Diagram below shows two points, M and N, on a Cartesian plane.



Transformation T is a translation $\left(\begin{array}{l}3\\ -1\end{array}\right)$ and transformation R is an anticlockwise rotation of 90^o about the centre (0, 2).
(i) State the coordinates of the image of point M under transformation R.
(ii) State the coordinates of the image of point N under the following transformations:
(a) T²,
(b) TR,

(b) Diagram below shows three pentagons, A, B and C, drawn on a Cartesian plane.


(i) C is the image of A under the combined transformation WV.
Describe in full the transformation:
(a) V    (b) W
(ii) Given A represents a region of area 12 m², calculate the area, in m², of the region represented by C.

Solution:
(a)

(b)


(b)(i)(a)
V: A reflection in the line x  = 8

(b)(i)(b)
W: An enlargement of scale factor 2 with centre (14, 0).

(b)(ii)
Area of B = area of A = 12 m²
Area of C = (Scale factor)² x Area of object
 = 2² x area of B
 = 2² x 12
 = 48 m²

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