ACT (Enhanced)MathematicsMedium
A cartographer is creating a map and needs to scale down a region. A forest that is 15 kilometers long on the ground needs to be represented as 30 centimeters on the map. If a river is 8 kilometers long in reality, how long should it be represented on the map?
- A16 cm
- B20 cm
- C24 cm
- D12 cm
Show answer & explanationAnswer & explanation
Correct answer: A. 16 cm
First, find the scaling factor. 15 km on the ground corresponds to 30 cm on the map. So, 1 cm on the map represents 15 km / 30 cm = 0.5 km per cm (or 30 cm / 15 km = 2 cm per km). Using the latter: 2 cm/km. For the river that is 8 km long: 8 km * 2 cm/km = 16 cm on the map.
Why the other options are wrong
- B. This would imply a scaling factor of 2.5 cm/km.
- C. This would imply a scaling factor of 3 cm/km.
- D. This would imply a different scaling factor, perhaps 1.5 cm/km.
Proportional Scaling
Proportional scaling involves maintaining the same ratio between dimensions when resizing an object or converting between different units/representations.
- A constant scaling factor (ratio) is applied.
- Used in maps, models, recipes, and image resizing.
- Can be expressed as a ratio or a unit rate.
Memory trick: Scale factor: Map over Real, then apply it again.