**Question 5:**

**(a)**Diagram below shows two points,

*M*and

*N*, on a Cartesian plane.

Transformation

**T**is a translation $\left(\begin{array}{l}\text{}3\\ -1\end{array}\right)$ 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)

**T**,

^{2}(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

**represents a region of area 12 m**

*A*^{2}, calculate the area, in m

^{2}, of the region represented by

**.**

*C*

*Solution:***(a)**

(b)

(b)(i)(a)

(b)

(b)(i)(a)

**V**: A reflection in the line

*x*= 8

(b)(i)(b)

(b)(i)(b)

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

**Area of**

(b)(ii)

(b)(ii)

*B*= area of

*A*= 12 m

^{2}Area of

*C*= (Scale factor)

^{2}x Area of object

= 2

^{2}x area of

*B*

= 2

^{2}x 12

= 48 m

^{2}

**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 m

^{2}.

Calculate the area, in m

^{2}, of the region represented by the shaded region.

*Solution:*

**(a)**

(b)

(i)(a)

(b)

(i)(a)

**V**: A reflection in the line

*EC.*

**$\begin{array}{l}\text{Scalefactor}=\frac{KL}{BC}=\frac{6}{2}=3\\ \text{W:Anenlargementofscalefactor3atcentre}J\text{.}\end{array}$**

(i)(b)

(i)(b)

**Area of**

(ii)

(ii)

*JKLANO*

= 3

^{2}x area of

*ABCDEF*

= 9 x 45

= 405 m

^{2}Area of the coloured region

= area of

*JKLANO*– area of

*ABCDEF*

= 405 – 45

= 360 m

^{2}