What are dilations and how can we apply them in real life? Give at least 2 examples.
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https://www.google.com/search?q=math%20dilations
Dilations are transformations that change the size of an object without altering its shape. They involve multiplying the coordinates of each point by a scaling factor, both horizontally and vertically. The scaling factor determines whether the figure is enlarged or reduced. Dilations can be useful in real-life applications to represent various scenarios of scaling and proportionality. Here are two examples:
1. Maps: When creating maps, it is common to use dilations to represent different scales. For instance, if you have a town map that you want to reproduce on a smaller scale, you can use a dilation to reduce the size of the entire map while maintaining the relative proportions of streets, buildings, and landmarks.
2. Industrial Design: Dilations are also used in industrial design to create scaled-down or scaled-up prototypes of products. Let's say a car manufacturer wants to design a smaller toy version of their popular model. They can use dilations to reduce the dimensions of the car while ensuring the same proportions and aesthetic features. Conversely, if they wish to produce an actual size prototype for testing, they can use dilations to enlarge the original model.
In both examples, dilations allow objects or images to be proportionally scaled, preserving the same overall shape and structure.