Final answer:
Dilations are used in real-world problems by applying a scale factor, which in this context refers to scaling objects to different sizes while keeping them proportional. An example is Calvin's map problem where a scale factor of 1/800 is used to determine the mapped distance between two points. Therefore, the correct option is B.
Step-by-step explanation:
Using dilations can help to solve real-world problems by applying a scale factor to adjust the size of objects while keeping them proportionally the same. The correct option for defining this process is Scale. Dilations can be beneficial in various fields such as cartography, architecture, and modeling. For instance, let's solve a problem where a student, Calvin, drew a map of his neighborhood using a scale factor of 1/800. To find the scaled distance between Calvin's house and his friend Frank's house on the map, we would use the scale factor and the actual distance.
Given:
Calvin's scale factor = 1/800
Actual distance = 80 meters
1 meter = 100 centimeters
Steps to solve:
1. Convert the actual distance from meters to centimeters: 80 meters * 100 cm/meter = 8000 centimeters.
2. Multiply the converted distance by the scale factor: 8000 centimeters * (1/800) = 10 centimeters.
Therefore, the distance between Calvin's house and Frank's house on the map would be 10 centimeters. This solution highlights the use of proportions in scaling real-life dimensions down to a manageable size for purposes such as creating a map.