Pregunta
6. A figure is dilated by a factor of 0.5 . By what factor will the area of the * 10 figure change? 0.25 0.5 1 1.5
Ask by Cole Colon. in the United States
Feb 03,2025
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The area of the figure will change by a factor of 0.25.
Solución
When a figure is dilated by a linear factor (also known as the scale factor), the area of the figure changes by the square of that factor.
Here's how it works:
- **Linear Scale Factor (k):** This is the factor by which each linear dimension of the figure is multiplied. In this case, \( k = 0.5 \).
- **Area Scale Factor:** The area of the figure changes by \( k^2 \).
Calculating the area scale factor:
\[
\text{Area Scale Factor} = k^2 = (0.5)^2 = 0.25
\]
**Therefore, the area of the figure will decrease by a factor of 0.25.**
**Answer:** 0.25
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When a figure is dilated by a factor of 0.5, each linear dimension of the figure is multiplied by 0.5. However, since area is a two-dimensional measurement, the area factor is the square of the scale factor. So, you would calculate (0.5)², which equals 0.25. Therefore, the area of the figure will change by a factor of 0.25. Think of it this way: if you have a square with a side length of 2 units, its area is 4 square units. If you then dilate it by 0.5, each side becomes 1 unit long, and its new area is 1 square unit. That’s a dramatic reduction – specifically, to a quarter of the original area!
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