**Question 13 (12 marks):**Diagram 13.1 shows three triangles

*RPQ*,

*UST*and

*RVQ*, drawn on a Cartesian plane.

**Diagram 13.1**

**(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}**Question 14 (12 marks):**

Diagram 14 shows a histogram which represents the mass, in kg, for a group of 100 students.

**Diagram 14**

(a)Based on Diagram 14, complete Table 14 in the answer space.

(a)

**Calculate the estimated mean mass of a student.**

(b)

(b)

**For this part of the question, use graph paper. You may use a flexible curve ruler.**

(c)

(c)

Using a scale of 2 cm to 10 kg on the horizontal axis and 2 cm to 10 students on the vertical axis, draw an ogive for the data.

**Based on the ogive drawn in**

(d)

(d)

**14**(c), state the third quartile.

Answer:

*Solution*:**(a)**

**(b)**

$\begin{array}{l}\text{Estimatedmeanmass}\\ =\frac{8110}{100}\\ =81.1\text{kg}\end{array}$

**(c)**

**(d)**

Third quartile

= 75th student

= 90.0 kg