**Question 9 (12 marks)**:

**(a)**Diagram 7.1 shows

*K*(5, 1) drawn on a Cartesian plane.

**Diagram 7.1**

Transformation

**T**is a translation $\left(\begin{array}{l}-3\\ \text{}4\end{array}\right)$

Transformation

**P**is a reflection in the line

*y*= 2.

State the coordinates of the images of point

*K*under each of the following transformations:

**(i) T**,

^{2}**(ii)**

**TP.**

**(b)**Diagram 7.2 shows two pentagons

*KLMNP*and

*QRSTU,*drawn on a Cartesian plane.

**Diagram 7.2**

(i)Pentagon

(i)

*QRSTU*is the image of pentagon

*KLMNP*under the combined transformation

**WV**.

Describe in full the transformation:

**(a)**

**V**,

**(b)**

**W**.

**It is given that pentagon**

(ii)

(ii)

*QRSTU*represents a region with an area of 90 m

^{2}.

Calculate the area, in m

^{2}, of pentagon

*KLMNP*.

*Solution:*

**(a)**

(i)

(i)

**TT**= K(5, 1) →

**T**→ K’(2, 5) ) →

_{1}**T**→ K’’(–1, 9)

_{2}**(ii) TP =**K(5, 1) →

**P**→ K’(5, 3) →

**T**→ K’’(2, 7)

**(b)**

(b)(i)(a)

(b)(i)(a)

**V**: 90

^{o}rotation in clockwise direction at point

*K*(3, 7).

**(b)(i)(b)**

**W**: Enlargement at point (1, 6) with scale factor 3.

**(b)(ii)**

Area of

*QRSTU*= (scale factor)

^{2}× area of object

Area of

*QRSTU*= 3

^{2}× Area of

*KLMNP*

90 m

^{2}= 9 × Area of

*KLMNP*

Area of

*KLMNP*= 90/9 =

**10 m**

^{2}