On the map, 3 MRT stations, Braddell (NS18), Caldecott (CC17) and Toa Payoh (NS19) are joined to form a triangle. construct the perpendicular bisector of the line connecting NS18 and NS19. construct the angle bisector at NS18. shade the region inside the triangle that is closer to the line joining NS18 and CC17 and is closer to NS18 than NS19. Which unit is the most value for money? Explain. Both John and Chiech are first-time HDB applicants as a married couple, they want to purchase a unit that is closest to the MRT station. Their combined monthly income is $7 500 and they wish to complete financing their home in 15 years' time using the HDB loan. John's friend, Janet, also Singaporean, is looking at purchasing unit B, which is 2 km away from her mum's place, under the Single's scheme. Janet is 38 this year and her monthly salary is $6 500. Assuming that they receive all the relevant grants and take up the maximum loan amount, suggest the number of years Janet should take to service the bank loan such that her interest paid is lower than John's and Chiech's. Justify any decisions you make and show your calculations clearly.

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Worked solution

12((a))((i))

1. Construct the perpendicular bisector of the line segment joining NS18 and NS19.

Set the compass to a radius greater than half of $NS18NS19$ . With centre $NS18$ , draw arcs above and below the line segment. Using the same radius and centre $NS19$ , draw arcs to intersect the first pair of arcs. Draw a straight line through the two arc intersection points.

Answer

The perpendicular bisector of $NS18NS19$ is constructed: a straight line crossing $NS18NS19$ at $90^\circ$ and passing through its midpoint.

12((a))((ii))

1. Construct the angle bisector at NS18.

Using a compass, draw an arc centred at $NS18$ cutting the two arms $NS18CC17$ and $NS18NS19$ . From these two intersection points, draw equal arcs to meet inside the triangle. Join $NS18$ to the point where the arcs meet. This line is the angle bisector of $\angle CC17\,NS18\,NS19$ .

Answer

The angle bisector at $NS18$ is constructed: a straight line from $NS18$ that divides $\nangle CC17\,NS18\,NS19$ into two equal angles.

12((a))((iii))

1. Identify and shade the intersection of the two required regions inside the triangle.

Points closer to $NS18$ than to $NS19$ lie on the $NS18$ side of the perpendicular bisector of $NS18NS19$ .

Points closer to the line $NS18CC17$ lie on the $NS18CC17$ side of the angle bisector at $NS18$ .

Therefore, shade the overlap of these two regions inside triangle $NS18CC17NS19$ .

Answer

Shade the part of the triangle that is on the $NS18$ side of the perpendicular bisector of $NS18NS19$ and on the $NS18CC17$ side of the angle bisector at $NS18$ .

12((b))

1. Compare the prices per unit area and identify the lowest rate.

Using the given psf values:

\begin{array}{c|c} \text{Unit} & \text{psf} \\ \hline A & 877 \\ B & 642 \\ C & 551 \\ D & 457 \end{array}

The lowest psf is $457$ , so Unit D gives the most area for each dollar spent.

Alternatively, checking by price per square metre:

$\frac{310000}{63}=4920.6\ldots \approx \$4921/\text{m}^2$

This is lower than the other units, so Unit D is the best value for money.

Answer

Unit D is the most value for money because it has the lowest price per square foot, $457$ psf. Equivalently, its price per square metre is about $\char36{}4921/\text{m}^2$ , which is the lowest among the four units.

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Worked solution

12((a))((i))

12((a))((ii))

12((a))((iii))

12((b))

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