An example of a factor scale is comparing two similar squares where one has a side length of 2 inches and the other has a side length of 4 inches, resulting in a scale factor of 1:2 from the smaller square to the larger square.
When discussing factor scales, it's important to understand the underlying concept. A scale factor is a ratio that describes how much a figure is enlarged or reduced. It's used extensively in geometry and mapmaking. Here's a breakdown:
-
Definition: A scale factor is a number used to multiply the dimensions of a figure to create a similar figure.
-
Enlargement vs. Reduction:
- If the scale factor is greater than 1, the figure is enlarged.
- If the scale factor is between 0 and 1, the figure is reduced.
- A scale factor of 1 indicates no change in size.
Let's elaborate on the square example:
- Smaller Square: Side Length = 2 inches
- Larger Square: Side Length = 4 inches
To find the scale factor from the smaller square to the larger square, we divide the side length of the larger square by the side length of the smaller square:
Scale Factor = (Side length of larger square) / (Side length of smaller square) = 4 inches / 2 inches = 2
This can be expressed as a ratio of 1:2, which means for every 1 unit of length on the smaller square, there are 2 units of length on the larger square.
Here's another example using different shapes:
Imagine two similar triangles:
- Smaller Triangle: Base = 3 cm, Height = 4 cm
- Larger Triangle: Base = 6 cm, Height = 8 cm
The scale factor can be calculated using either the base or the height:
Scale Factor (using base) = 6 cm / 3 cm = 2
Scale Factor (using height) = 8 cm / 4 cm = 2
Again, the scale factor is 2 (or 1:2).
In summary, a factor scale demonstrates the proportional relationship between corresponding dimensions of similar figures, indicating how much larger or smaller one figure is compared to the other.
