**Further Practice:**

**Transformation III, Long Questions (Question 1)**

**Question 1:**

**(a)**Transformation

**T**is a translation $\left(\begin{array}{l}-4\\ \text{}2\end{array}\right)$ and transformation

**P**is an anticlockwise rotation of 90

^{o}about 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

**T**.^{2}**(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 m

^{2}.

Calculate the area, in m

^{2}, 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 m^{2}Area of

*JKLM*= (Scale factor)^{2}× Area of object = 3

^{2}× area of*EFGH* = 3

^{2}× 18 = 162 m

^{2}Therefore,

Area of the shaded region

= Area of

*JKLM*– area of*EFGH*= 162 – 18

=

**144 m**^{2}