**Question 4:**Diagram below shows three triangles

*RPQ*,

*UST*and

*RVQ*, drawn on a Cartesian plane.

**(a)**Transformation

**R**is a rotation of 90

^{o}, clockwise about the centre

*O*.

Transformation

**T**is a translation $\left(\begin{array}{l}2\\ \text{3}\end{array}\right)$ .

State the coordinates of the image of point B under each of the following transformations:

(i) Translation

**T**,

^{2}(ii) Combined transformation

**TR**.

**(b)**

**(i)**Triangle

*UST*is the image of triangle

*RPQ*under the combined transformation

**VW**.

Describe in full the transformation:

(a)

**W**(b)

**V**

(ii) It is given that quadrilateral

*RPQ*represents a region of area 15 m

^{2}.

Calculate the area, in m

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

*Solution*:**(a)**

**(i)**(–5, 3) →

**T**→ (–3, 6) ) →

**T**→ (–1, 9)

**(ii)**(–5, 3) →

**R**→ (3, 5) →

**T**→ (5, 8)

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

**W**: A reflection in the line

*URQT.*

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

$\begin{array}{l}\text{Scalefactor}=\frac{US}{RV}=\frac{6}{2}=3\\ \text{V:Anenlargementofscalefactor3atcentre}\left(-4,2\right)\end{array}$

**(b)(ii)**

Area of

*UST*= (Scale factor)

^{2}x Area of

*RPQ*

= 3

^{2}x area of

*RPQ*

= 3

^{2}x 15

= 135 m

^{2}

Therefore,

Area of the shaded region

= Area of

*UST*– area of

*RPQ*

= 135 – 15

=

**120 m**

^{2}