A topographical map drawn to a Representative Fraction (R.F.) scale of 1 : 50,000 is enlar… — JAMB UTME

A topographical map drawn to a Representative Fraction (R.F.) scale of $1 : 50,000$ is enlarged to twice its original linear dimensions. What is the scale of the new enlarged map?

A
$1 : 100,000$
$1 : 25,000$ Answer
C
$1 : 12,500$
D
$1 : 200,000$

Answer

The scale of the new enlarged map is

1 : 25,000

Enlarging a map increases its scale, making the scale denominator smaller. When a map is enlarged to twice its linear size (

2\times

), the denominator of the original Representative Fraction (

50,000

) is divided by

2

, yielding a new scale of

1 : 25,000

Step-by-Step Solution

Identify the original scale denominator and the linear enlargement factor.

Original scale denominator =

50,000

; Linear factor (

k

) =

2

Map enlargement alters the scale denominator inversely proportional to the linear change.

Calculate the new scale denominator by dividing the original denominator by the linear enlargement factor.

New denominator =

\frac{50,000}{2} = 25,000

Enlarging a map makes features larger on paper, which corresponds to a larger scale with a smaller denominator.

State the new Representative Fraction (R.F.) scale.

New scale =

1 : 25,000

The new R.F. expresses the enlarged relationship between map distance and ground distance.

Key Concept

Linear Map Enlargement Scale Conversion

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

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