**Further Practice:**

**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}
(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}x Area of object
= 3

^{2}x area of*EFGH*
= 3

^{2}x 18
= 162 m

^{2}
Therefore,

Area of the shaded region

= Area of

*JKLM*– area of*EFGH*
= 162 – 18

=

**144 m**^{2}