A proposed power transmission line measures 14.4\text{ cm} on Map X, which is drawn to a R… — JAMB UTME

A proposed power transmission line measures $14.4\text{ cm}$ on Map X, which is drawn to a Representative Fraction (RF) scale of $1 : 250,000$ . The same power line is subsequently transferred to Map Y, where its total path is measured across two contiguous sections: a straight stretch of $8.0\text{ cm}$ and a curved section of $10.0\text{ cm}$ . What is the denominator of the Representative Fraction (RF) scale of Map Y?

Answer: 200000

Answer

The denominator of the Representative Fraction (RF) scale of Map Y is 200,000 (representing a scale of

1 : 200,000

Because ground distance remains constant, the actual distance is

14.4\text{ cm} \times 250,000 = 3,600,000\text{ cm}

. On Map Y, the total route length is

8.0\text{ cm} + 10.0\text{ cm} = 18.0\text{ cm}

. Dividing

3,600,000\text{ cm}

18.0\text{ cm}

gives a scale denominator of

200,000

, which corresponds to a scale of

1 : 200,000

Step-by-Step Solution

Calculate the actual ground distance using the length on Map X and its scale

Ground distance =

14.4\text{ cm} \times 250,000 = 3,600,000\text{ cm}

(or

36\text{ km}

)

Map scale defines the relationship between map distance and ground distance:

\text{Ground distance} = \text{Map distance} \times \text{Scale denominator}

Determine the total measured length of the route on Map Y

Total distance on Map Y =

8.0\text{ cm} + 10.0\text{ cm} = 18.0\text{ cm}

The entire feature consists of two contiguous sections that must be added together.

Calculate the RF scale denominator of Map Y

RF denominator =

\frac{3,600,000\text{ cm}}{18.0\text{ cm}} = 200,000

The scale denominator is the ratio of ground distance to map distance when both are expressed in the same unit.

Key Concept

Ground distance conservation across maps of differing scales and multi-segment scale denominator calculation.

Estimated Time:2m 30s

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