Final answer:
A scale drawing uses a scale factor to accurately represent the size of objects in a smaller or larger form while preserving their proportions. To use a scale factor, multiply the scale drawing measurement by the scale to get the actual size. For instance, with a scale of 1:200, a map distance of 1.7 centimeters would correspond to an actual distance of 340 meters.
Step-by-step explanation:
The question you're asking about involves creating a scale drawing with a specific scale factor. This key concept in mathematics, particularly in geometry, allows us to represent real-world sizes on paper or models in a much smaller or larger size yet maintaining the proportions of the original dimensions.
How to Use a Scale Factor
Here's an example problem to illustrate the use of a scale factor:
- Calvin drew a map of his neighborhood. The scale factor he used was 1/800.
- To find the scaled distance on the map, you'd multiply the actual distance by the scale factor. So if Calvin's house and his friend's house are 80 meters apart, the distance on the map would be 80 meters multiplied by 1/800, resulting in a distance of 0.1 meters, or 10 centimeters, on his scale drawing.
When you're using a scale where 1 box = 20 meters, it means that each box on the drawing would represent an area that is 20 meters in the real world. So, if you have a distance of 1.7 centimeters on the map, and you were given the scale 1:200 (or 1 centimeter = 200 meters), you would calculate the real distance by multiplying 1.7 by 200, which would give you 340 meters as the actual distance between the sandbox and jungle gym.