Question

a map is scaled with 1 cm : 400 m. if a road measures 4.5 cm on the map, what is its actual length?
a. 2000 m
b. 1800 m
c. 1600 m
d. 2200 m
how would failing to maintain proportional relationships when creating a scale drawing affect its accuracy?
a. the scale drawing would be smaller than expected.
b. the drawing would be distorted but still usable.
c. the scale factor would remain the same, but measurements would be inaccurate.
d. the drawing would no longer accurately represent the actual object.

Explanation:

First Question (Map Scale Calculation)

Step1: Understand the scale

The scale is \(1\,\text{cm} : 400\,\text{m}\), meaning \(1\,\text{cm}\) on the map represents \(400\,\text{m}\) in actual.

Step2: Calculate actual length

For \(4.5\,\text{cm}\) on the map, actual length \(= 4.5\times400\)
\(= 1800\,\text{m}\)

Proportional relationships in scale drawings ensure the drawing is a true representation. Failing to maintain them means the drawing's proportions (like lengths, angles, etc.) won't match the actual object, so it won't accurately represent it. Option a is wrong as distortion can be in any way, not just smaller. Option b is wrong as distortion can make it unusable. Option c is wrong as scale factor would change or be inconsistent.

Answer:

b. 1800 m

Second Question (Effect of Proportional Relationships in Scale Drawings)