Real-World Examples of Dilations: Exploring Scale in Everyday Life

📚 Quick Study Guide

• 📐 Dilation: A transformation that changes the size of a figure, but not its shape.
• 🎯 Scale Factor (k): The ratio of the new image size to the original size. If $k > 1$, it's an enlargement; if $0 < k < 1$, it's a reduction.
• 📍 Center of Dilation: The fixed point from which the figure is enlarged or reduced.
• ➕ Formula: If a point $(x, y)$ is dilated by a scale factor $k$ from the origin, the new point is $(kx, ky)$.
• 🖼️ Real-world Examples: Photographs, maps, architectural blueprints, and even your pupils dilating in response to light!

🧪 Practice Quiz

1. What happens to a figure when it undergoes a dilation with a scale factor of 0.5?
   1. It stays the same size.
   2. It becomes twice as large.
   3. It becomes half as large.
   4. It rotates.
2. A blueprint of a house is created using a scale factor of 1/20. If a wall is actually 5 meters long, how long will it be on the blueprint?
   1. 1 meter
   2. 0.25 meter
   3. 0.5 meter
   4. 0.1 meter
3. Which of the following is NOT an example of dilation in real life?
   1. A map showing a city.
   2. A photo being enlarged.
   3. A reflection in a mirror.
   4. A microscope enlarging cells.
4. If a square with sides of length 2 cm is dilated by a scale factor of 3, what is the area of the new square?
   1. 6 cm²
   2. 12 cm²
   3. 18 cm²
   4. 36 cm²
5. The pupils in your eyes dilate to adjust to different light levels. Is this an example of enlargement or reduction when going from bright light to dim light?
   1. Enlargement
   2. Reduction
   3. No dilation occurs
   4. Rotation
6. A triangle has vertices at (1, 1), (2, 1), and (1, 3). If it is dilated by a scale factor of 2 from the origin, what are the coordinates of the new vertices?
   1. (2, 2), (4, 2), (2, 6)
   2. (1, 1), (2, 1), (1, 3)
   3. (0.5, 0.5), (1, 0.5), (0.5, 1.5)
   4. (3, 3), (4, 3), (3, 5)
7. An architect creates a model of a building with a scale factor of 1/100. If the model is 0.5 meters tall, how tall will the actual building be?
   1. 5 meters
   2. 50 meters
   3. 0.005 meters
   4. 200 meters