**Question 11:**

Diagram below shows the route of a Negaraku Run.

The route of male participants is

*PQUT*while the route for female participants is

*QRST*.

*QR*is parallel to

*UT*whereas

*UQ*is parallel to

*SR*.

(a) Given the distance between point

*Q*and point

*R*is 9 km, state the coordinates of point

*R*.

(b) It is given that the male participants start the run at point

*P*and the female participants at point

*Q*.

Find the difference of distance, in km, between the male and female participants.

*Solution*:**(a)**

*R*= (9, 1)

**(b)**

Route of male participants

=

*PQ*+

*QU*+

*UT*

= 10 + 7 + 7

= 24 km

Route of female participants

=

*QR*+

*RS*+

*ST*

= 9 + 7 + 2

= 18 km

Difference in distance

= 24 – 18

= 6 km

**Question 12:**

Diagram below shows a parking lot in the shape of trapezium,

*RSTU*. Two coordinates from the trapezium vertices are

*R*(–30, –4) and

*S*(20, –4).

(a) Given the distance between vertex

*S*and vertex

*T*is 22 units.

State the coordinates of vertex

*T*.

(b) Given the area of the parking lot is 946 unit

^{2}, find the coordinates of

*U*.

*Solution*:**(a)**

*y-*coordinates of

*T =*–4 + 22 = 18

*T*= (20, 18)

**(b)**

$\begin{array}{l}\text{Areaoftrapezium}=946{\text{unit}}^{2}\\ \frac{1}{2}\times \left(UT+RS\right)\times ST=946\\ \frac{1}{2}\times \left(UT+50\right)\times 22=946\\ UT+50=\frac{946\times 2}{22}\\ UT+50=86\\ UT=36\\ \\ x-\text{coordinateofpoint}U=20-36=-16\\ y-\text{coordinateofpoint}U=18\\ U=\left(-16,18\right)\end{array}$