Question

Suppose you have a map that uses the scale 1 cm to 200 m. You draw a new map of the same place using the scale 1 cm to 20 m.

1. How does your new map compare to your original map in terms of length?
2. How does the area change between your new map and your original map?

Answer 1

The new map scale of 1 cm to 20 m means lengths are 10 times greater, and the area is 100 times greater on the new map compared to the original map with a scale of 1 cm to 200 m.

Step-by-step explanation:

When you change the scale of a map from 1 cm to 200 m to a scale of 1 cm to 20 m, the new map's scale factor has increased by a factor of 10. This means that any given length on the new map is 10 times larger than it was on the original map. Therefore, a 1 cm line on the original map that represented 200 m of actual distance will now measure 10 cm on the new map to represent the same distance. As for the area, since the length dimensions are scaled up by a factor of 10, the area represented on the new map will be scaled by a factor of 102 (since the area is a two-dimensional measurement and scales with the square of the linear dimensions). This means the area would be 100 times larger on the new map than the original map. For instance, if a park that's 1 cm2 on the original map is actually 40,000 m2 in reality, on the new map it would be represented by a 10 cm × 10 cm square for the same area.