Real-World Examples of Dilations: Applications in Daily Life

📚 Quick Study Guide

• 📏 Definition: Dilation is a transformation that changes the size of a figure without changing its shape.
• 🔍 Scale Factor: The ratio of the new size (image) to the original size (pre-image). If the scale factor is greater than 1, it's an enlargement; if it's between 0 and 1, it's a reduction.
• 📍 Center of Dilation: The fixed point about which the figure is enlarged or reduced.
• 🔢 Formula: If a point $(x, y)$ is dilated by a scale factor $k$ with the center of dilation at the origin, the new point is $(kx, ky)$.
• 💡 Real-World Applications: Include resizing images, creating maps, architectural blueprints, and even the human eye.

🧪 Practice Quiz

1. A map is created where 1 inch represents 25 miles. This is an example of what?
   1. A) Translation
   2. B) Rotation
   3. C) Dilation
   4. D) Reflection
2. A photographer wants to enlarge a 4x6 inch photo to an 8x12 inch photo. What is the scale factor of this dilation?
   1. A) 1
   2. B) 2
   3. C) 3
   4. D) 4
3. The human eye's pupil dilates to adjust to changes in light. If the pupil's diameter changes from 2mm to 6mm, what is the scale factor of dilation?
   1. A) 1/3
   2. B) 2
   3. C) 3
   4. D) 4
4. In architecture, blueprints are scaled-down versions of actual buildings. If a blueprint shows a room as 3 inches wide, representing an actual width of 15 feet, what is the scale factor (inches to feet)?
   1. A) 1/5
   2. B) 5
   3. C) 1/60
   4. D) 60
5. A microscope enlarges a cell 100 times its original size. This is an example of:
   1. A) Reduction
   2. B) Reflection
   3. C) Enlargement
   4. D) Rotation
6. A computer screen displays an image that can be zoomed in or out. If you zoom in on an image by a factor of 1.5, what type of transformation is this?
   1. A) Reflection
   2. B) Dilation
   3. C) Rotation
   4. D) Translation
7. A company logo is resized for use on a business card. The original logo is 4 inches wide, and the new logo is 1 inch wide. What is the scale factor of the dilation?
   1. A) 1
   2. B) 4
   3. C) 1/2
   4. D) 1/4