Scales and Direction

ICSE Class 10 · Geography · Chapter 3

What this chapter covers

Why a map needs a scale
Statement scale
Representative Fraction
Linear Scale
Comparing the three types of scale
Measuring direct distance on a map
Calculating area using the scale
Direction on a topographical map
The eight cardinal points
Marking directions between different locations

Key points

The scale of a map is the ratio between map distance and ground distance.
A statement scale gives the scale in words, such as "2 cm to 1 km"; it is easy to read but tied to its units.
A Representative Fraction, such as 1:50,000, has no units and can be read in any unit, so it is the universal form.
A linear scale is a divided bar; it gives distances without arithmetic and stays correct when the map is enlarged or reduced.
On a 1:50,000 toposheet, 1 cm represents 0.5 km, 2 cm represents 1 km, and one tenth of a grid square is 100 m.
To change an RF into km per cm, divide the denominator by 100,000; to change a statement into an RF, express the ground distance in centimetres.
Direct distance is the straight-line distance between two points; measure it with a ruler and the scale or a divider and the linear scale, and always give the unit.
Area is found by counting full grid squares; each full square on a 1:50,000 sheet covers 1 km².
Count the spaces between grid lines, not the lines: subtract the easting and northing values.
North is at the top of a toposheet; eastings increase towards the east and northings increase towards the north.
The eight directions are N, NE, E, SE, S, SW, W and NW, each 45^° apart.
In a direction question, stand mentally at the starting place; the reverse direction is always the opposite point.

Questions answered

Define the scale of a map.

The scale of a map is the ratio between a distance measured on the map and the corresponding distance on the ground.

Name the three types of scale printed on a Survey of India toposheet.

Statement scale, Representative Fraction (RF) and linear scale.

Why is the Representative Fraction called a universal scale?

It has no units, so the same ratio can be read in centimetres, inches or any other unit by a reader in any country.

Give one advantage of the linear scale over the other two types.

It stays correct when the map is enlarged or reduced, because the bar changes size along with the map.

Convert the RF 1:50,000 into a statement scale.

1 cm represents 0.5 km, which is the same as 2 cm to 1 km.

A map has the statement scale "1 cm to 2 km". Find its RF.

2 km = 200,000 cm, so the RF is 1:200,000.

On a 1:50,000 sheet, the distance between two villages measures 9.2 cm. Find the direct ground distance.

9.2 × 0.5 = 4.6 km.

What is meant by direct distance?

Direct distance is the straight-line distance between two points on the map, measured as the crow flies without following roads or rivers.

Past board exam questions

ICSE 2023 sample paper · 2 marks

What advantage does Representative Fraction have over Statement scale?

Show answer

A Representative Fraction (e.g. 1:50,000) has no units, so it is universal: it can be read and understood in any system of measurement (cm, inches, km, miles) and in any language, whereas a statement scale (e.g. 1 cm represents 1 km) is tied to particular units and is understood only by those who know those units.

ICSE 2020 board paper · 2 marks

With reference to the Survey of India Map sheet No. 45D/10, answer the following: What is the area in kilometre square of the region between 06 and 09 Eastings and 22 and 27 Northings?

Show answer

On a 1:50,000 sheet each grid square is 1 km × 1 km. East-west: 09 − 06 = 3 km; north-south: 27 − 22 = 5 km. Area = 3 km × 5 km = 15 sq. km.

ICSE 2020 board paper · 2 marks

With reference to the Survey of India Map sheet No. 45D/10, answer the following: What is the compass direction of? (i) Idarla (0825) from Bhamra (0420). (ii) Dhana (0623) from Amarapura (0124).

Show answer

(i) Idarla (0825) lies 4 km east and 5 km north of Bhamra (0420), so Idarla is to the North-East of Bhamra. (ii) Dhana (0623) lies 5 km east and about 1 km south of Amarapura (0124), so Dhana is to the East of Amarapura.

ICSE 2019 board paper · 2 marks

With reference to the Survey of India Map sheet No. 45D/10, answer the following: Calculate the area of the region between 16 and 19 Eastings and 18 and 22 Northings. Give your answer in kilometre square.

Show answer

On a 1:50,000 sheet each grid square is 1 km × 1 km. East-west: 19 - 16 = 3 km; north-south: 22 - 18 = 4 km. Area = 3 km × 4 km = 12 km².

ICSE 2018 sample paper · 2 marks

Study the extract of the survey of India map sheet No 45 D/10 and answer the following questions (Easting 11-21, Northings 13-23): What is the area in square Kms of the region enclosed within Easting 13 and 18 and Northing 17 and 21?

Show answer

On a 1 : 50,000 sheet each grid square is 1 km × 1 km. East-west: 18 − 13 = 5 km; north-south: 21 − 17 = 4 km. Area = 5 km × 4 km = 20 sq km.

ICSE 2018 sample paper · 2 marks

Study the extract of the survey of India map sheet No 45 D/10 and answer the following questions (Easting 11-21, Northings 13-23): What is the R.F. of this map? What does it mean?

Show answer

R.F. = 1 : 50,000. It means that 1 unit of distance on the map represents 50,000 of the same units on the ground, i.e. 1 cm on the map = 50,000 cm = 0.5 km on the ground.

ICSE 2011 sample paper · 2 marks

Study the extract of the survey of India Map Sheet No. 45 D/7 (Eastings 91 to 01 and Northings 73 to 83) and answer the following questions: (i) What is meant by the term R F? (ii) What is the total area of the given map extract in kilometres?

Show answer

(i) R F (Representative Fraction) is the scale of a map expressed as a fraction or ratio, in which 1 unit of distance on the map represents a stated number of the same units on the ground, e.g. 1 : 50,000 means 1 cm on the map = 50,000 cm (0.5 km) on the ground. (ii) On a 1 : 50,000 sheet each grid square is 1 km × 1 km. East-west: Eastings 91 to 01 = 10 km; north-south: Northings 73 to 83 = 10 km. Area = 10 km × 10 km = 100 sq km.