Let's break down the difference between the scale factor and the ratio of perimeters when we're talking about dilations. While they're related, it's important to understand how they differ.
The scale factor is the ratio of the length of a side on the image to the length of the corresponding side on the original figure (pre-image) after a dilation. It tells you how much larger or smaller the image is compared to the original.
Mathematically, if you have a pre-image side length of $x$ and an image side length of $y$, the scale factor, $k$, is:
$k = \frac{y}{x}$
The ratio of perimeters is the ratio of the perimeter of the image to the perimeter of the original figure (pre-image) after a dilation.
If the perimeter of the pre-image is $P_1$ and the perimeter of the image is $P_2$, then the ratio of perimeters is:
$\text{Ratio of Perimeters} = \frac{P_2}{P_1}$
| Feature | Scale Factor | Ratio of Perimeters |
|---|---|---|
| Definition | Ratio of corresponding side lengths in image and pre-image. | Ratio of the perimeter of the image to the perimeter of the pre-image. |
| Calculation | $\frac{\text{Image Side Length}}{\text{Pre-image Side Length}}$ | $\frac{\text{Perimeter of Image}}{\text{Perimeter of Pre-image}}$ |
| Value | A single number representing enlargement or reduction. | A single number representing how much larger or smaller the perimeter becomes. |
| Relationship | Directly used to find the new side lengths. | Equal to the scale factor. |
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀