By studying this lesson, you will be able to,

● express the location of a place from a given location in terms of the eight directions and

● identify the horizontal and the vertical.

8.1 The main directions

• Strong winds in the North-eastern shores of the island – A weather notification

• It is auspicious to light the hearth at 8.05 a.m. while facing the East

– a New Year Custom

• A meteor shower can be observed in the south-western sky between 3 a.m. and 5 a.m. – A news item.

The above are several instances in day to day life, where directions are mentioned. Thus, knowledge of directions is required when conducting daily activities.

Now, let us recall what was learnt earlier regarding the four main directions.

When directions are drawn in a book, the following convention is used.

The North is indicated in maps and in house plans by the notation ''⬆️ '' N .

A compass can be used to accurately find the directions from a given position. Let us now consider how it works.

When a compass is placed on a flat surface, the red needle points in the direction of the North. When the compass is rotated such that the letter N is aligned with the point of the red needle, the remaining directions too are indicated by the compass.

Let us identify the location of the following in the figure in terms of directions.

According to the above figure,

1. the tree is to the north of the child.

2. the well is to the east of the child.

3. the house is to the west of the child.

4. the gate is to the south of the child.

5. the child is facing the South.

6. the child and the tree are both to the north of the gate.

Exercise 8.1

(1) Fill in the blanks by considering the following figure.

8.2 Sub directions

Apart from these four main directions, let us now learn about four other sub directions.

* The direction which divides the right angle between the North and the East exactly into two as shown in the figure is the North-east.

* The direction which divides the right angle between the East and the South exactly into two as shown in the figure is the South-east.

* The direction which divides the right angle between the South and the West exactly into two as shown in the figure is the South-west.

* The direction which divides the right angle between the West and the North exactly into two as shown in the figure is the North-west.

Eight directions - North, East, South, West, North-east, South-east, South-west and North-west.

Now, let us study further about directions by considering several places that are marked in the following map of Sri Lanka.

Trincomalee is to the north-east of Dambulla.

Dambulla is to the south-west of Trincomalee.

Exercise 8.2

(1) Upul’s house and various places around his house are shown below.

(a) Complete the following table by writing the direction in which each place is located with respect to the house.

(b) Copy the following sentences and fill in the blanks.

(i) While the post office is located to the ............of the house, the house is located to the .....................of the post office.

(ii) To go from the bus halt to the post office, one should travel towards the ............and when returning from the post office to the bus halt, one should travel towards the .....................

(iii) While the hospital is located to the ............ of the post office, the ......is located to the south-west of the hospital.

(iv) While the ..................is located to the north-east of the temple, the ............ is located to the north of the hospital.

(v) If a person travels from the temple towards the .............., he would come across the house. If he travels from the house towards the west, he would come across the ..................... To reach the temple again from the bus halt, he should travel towards the ..................

(2) The square grid given below illustrates several places that are located on a flat ground.

A rabbit who starts moving from the place named A, travels along the path indicated by the arrows eating Desmodium (Undupiyaliya) and returns again to A.

(3) Answer the following questions by considering the cities marked on the given map.

(4) A soldier who was being trained to walk through forests was taken to a rocky surface in a forest and given the following instructions based on which he had to complete his journey.

(i) After travelling 500 m towards the east of the rocky surface, you will come across a footbridge that lies across a stream.

(ii) After crossing the footbridge, and travelling 800 m towards the north-east, you will come across a waterfall.

(iii) When you travel a distance of 600 m from the waterfall towards the south-east, you will come across a Kitul tree.

(iv) When you travel 750 m towards the south-west from the Kitul tree, you will come across a cave.

(v) By travelling 800 m from the cave towards the north-west you will return to the camp.

Based on the information that has been provided to the soldier, draw a rough diagram of the path that he should take.

8.3 The horizontal and the vertical

Apart from the directions we have talked about so far, there are two other concepts which are necessary to describe the location of an object. These are the horizontal and the vertical.

The surface of the water in a large basin is considered to be horizontal when the water is still.

A flat surface which is not inclined, is said to be in a horizontal plane.

Any straight line which lies on a horizontal plane is called a horizontal line.

Any two points which lie on a horizontal plane, are said to be at the same level.

Consider several small balls on a horizontal plane. We say that these balls are in the same horizontal level.

Take a string which has a small weight tied to it at one end, and hold it by the other end. Wait until the string stops moving. Then the line along which the string lies is a vertical line.

If a plane contains a vertical line, then it is a vertical plane.

Any straight line which lies on a horizontal plane is a horizontal line. But any straight line which lies on a vertical plane is not necessarily a vertical line.

Let us identify several other vertical and horizontal positions.

A spirit level is used to determine whether a plane surface is horizontal.

A plumb is used to identify vertical positions.

Exercise 8.3

(i) The pigeon hole with pigeon A lies horizontal to the pigeon hole with pigeon ................

(ii) The pigeon hole with pigeon B lies vertically below the pigeon hole with pigeon .......................

(iii) The pigeon hole with pigeon F lies .......................... to the pigeon hole with pigeon E.

(iv) The pigeon hole with pigeon C lies ....................... the pigeon hole with pigeon D.

(v) The pigeon holes with pigeons B, D and G lies on the same ............ plane.

Revision Exercise

(1) For the number 53 428,

(i) write down the place value corresponding to the position of each digit.

(ii) write down the value represented by each digit.

(2) "One hundred fifty five billion eight million two hundred five thousand four hundred eight" Write down this number in the standard form in digits.

(3) Write down each of the following numbers in standard form. Name the number too.

(i) 750037 (ii) 1024839

(4) Sri Lanka got independence from the English regime on 4th February 1948. Write down this date in standard form.

(5) Write down the digits suitable for the blanks boxes.

(i) 85 +🔲🔲🔲= 232 

(ii) 3156 -🔲🔲🔲 = 2825

(6) The daily wage of a labourer is Rs 750. What is the total amount that should be paid, if 8 labourers are hired for 10 days?

(7) Round off the following numbers to the nearest multiple of ten.

(i) 64 (ii) 97 (iii) 45

(8) Fill in the blanks.

(i) 67 651 × 1 = .............. (ii) 875 × 37 = 37 × .............

(iii) 31 611 × 0 = .............. (iv) 0 ÷ 31 611 = ......................

(v) 28 971 ÷ 1 = .............. (vi) 478 × 1000 = ......................

(vii) 98 714 ÷ ... = 98 714 (viii) ......... × 1 = 3325

(ix) If the number 67 000 is divided by 10, the quotient is ...... and

the remainder is ......... .

(9) Simplify.

(i) 4343 + 75 (ii) 6848 - 959 (iii) 3328 × 25 (iv) 3227 ÷ 19

(10) Fill in the blanks in the given table.

(12) Fill in the blanks by considering the following figure.

(i) The post office is located to the .........of the bus halt.

(ii) The bus halt is located to the ......... of the police station.

(iii) The ............. and ............. are located to the north of the bank.

(13) (i) Draw a number line and represent the integers 6 and - 4 on it.

(ii) Write down all the integers between these two integers.

(iii) Fill in the blanks using either the sign > or the sign <.

(a) - 4 ...3 (b) 0 ... - 3

(c) - 3 .... - 4 (d) -1 ... 0

(b) Four corners of a square shaped land on a flat landscape are

named A, B, C and D as shown in the figure. D lies in the

direction of the south when observed from A. One can walk

along straight paths between the four corners. Write down the

directions, that someone should walk in each of the following

situations.

(15) (i) When a whole number is rounded off to the nearest multiple

of ten, the number 40 is obtained. Write down all the possible

numbers that the above whole number could be.

(ii) Write down two situations, where estimation is used in

day to day life.

(iii) Since the railway track was blocked due to an earth slip, it

was decided to bring the passengers to the next main railway

station by buses. A bus can carry about 45 passengers. How

many buses should be used to bring 673 passengers at the

same time?

(16) It usually takes 3 hours to reach the Katunayake Airport from

Galle along the old Galle road. This journey can be done in 1 hour

and 20 minutes using the new Galle-Katunayake road.

(i) Express the time in hours and minutes, that is saved by using

the new road for this journey.

(ii) Suppose that a passenger should be in the airport by 2.00 p.m.. Write down the time by the 12 hour clock that the passenger

should leave from Galle,

(a) if he plans to use the new road.

(b) if he plans to use the old road.

(iii) The flight that passenger should take departs at 17:10. Write

down this time by the 12 hour clock.