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Zorluk: OrtaMap Enlargement and Reduction

A straight segment of a proposed highway measures 10 cm10\text{ cm} on a topographic map drawn at a scale of 1:50,0001 : 50,000. On a newly redrawn map, the same segment of highway measures 25 cm25\text{ cm}. What is the Representative Fraction (R.F.) scale of the new map?

  1. 1:20,0001 : 20,000Cevap
  2. B
    1:125,0001 : 125,000
  3. C
    1:8,0001 : 8,000
  4. D
    1:200,0001 : 200,000

Cevap

The Representative Fraction (R.F.) of the new enlarged map is 1:20,0001 : 20,000.
The correct scale is 1:20,0001 : 20,000. When a map features are enlarged from 10 cm10\text{ cm} to 25 cm25\text{ cm}, the linear dimension increases by a factor of 2.52.5. Because enlargement increases map scale (making features appear larger), the Representative Fraction denominator decreases by dividing the original denominator by 2.52.5, giving 50,000/2.5=20,00050,000 / 2.5 = 20,000.

Adım Adım Çözüm

1
Determine the linear enlargement factor
Linear Enlargement Factor = New DistanceOriginal Distance=25 cm10 cm=2.5\frac{\text{New Distance}}{\text{Original Distance}} = \frac{25\text{ cm}}{10\text{ cm}} = 2.5
Map enlargement increases map distance proportionally by a linear multiplier.
2
Calculate the new Representative Fraction (R.F.) scale denominator
\text{New Denominator} = \frac{\text{Original Denominator}}{\text{Enlargement Factor}} = \frac{50,000}{2.5} = 20,000
Enlarging a map produces a larger scale, which corresponds to a smaller scale denominator.
3
State the new R.F. scale
New R.F. scale = 1:20,0001 : 20,000
The Representative Fraction expresses the scale ratio with a numerator of 1.

Anahtar Kavram

Map Enlargement Linear Scale Calculation
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Konular

Map Enlargement and Reduction

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