Question

5 the distance between vancouver and winnipeg is approximately 1850 km in a straight line. the distance on a map is 3.7 cm. write a scale statement for the map. what scale factor was used to make the map?

Explanation:

Step1: Convert km to cm

Since \(1\space km = 100000\space cm\), then \(1850\space km=1850\times100000 = 185000000\space cm\).

Step2: Find scale statement

The scale statement is the ratio of map distance to actual distance. So, \(\frac{3.7\space cm}{185000000\space cm}=\frac{1}{50000000}\) (dividing numerator and denominator by \(3.7\), \(185000000\div3.7 = 50000000\)).

Step3: Determine scale factor

The scale factor is the ratio of map distance to actual distance, which we found as \(\frac{1}{50000000}\), so the scale factor is \(1:50000000\) (or \(\frac{1}{50000000}\)).

Answer:

Scale statement: \(1\space cm:50000000\space cm\) (or \(1\space cm:500\space km\) since \(50000000\space cm = 500\space km\)), Scale factor: \(\frac{1}{50000000}\) (or \(1:50000000\))