The linear scale factor of two similar shapes is found by dividing the length of a side on one shape by the length of the corresponding side on the other shape.
To elaborate, similar shapes are shapes that have the same angles but different sizes. The ratio of corresponding sides in similar shapes is constant; this constant ratio is the linear scale factor (sometimes called the scale factor or similarity ratio).
Here's how you can find it:
- Identify Corresponding Sides: Make sure you are comparing sides that are in the same position on both shapes.
- Divide: Divide the length of a side on the new shape (the image) by the length of the corresponding side on the original shape (the pre-image).
Scale Factor = (Length of side on Image) / (Length of corresponding side on Pre-image)
Example:
Suppose you have two similar triangles. Triangle A has a side length of 5 cm, and the corresponding side on Triangle B has a length of 10 cm.
Scale Factor = 10 cm / 5 cm = 2
This means that Triangle B is twice the size of Triangle A. Every side on Triangle B is twice as long as the corresponding side on Triangle A.
Important Considerations:
- The linear scale factor can be greater than 1 (enlargement), less than 1 (reduction), or equal to 1 (congruent shapes).
- It's important to be consistent in your division. If you always put the new shape's side length on top, you will always get the scale factor that describes how the shape has been transformed from the original.
- If you know the scale factor, you can find the length of any side on one shape if you know the length of the corresponding side on the other shape.
In summary, the linear scale factor is a ratio that describes how much larger or smaller a similar shape is compared to the original shape, and is calculated by dividing the length of a side on one shape by the length of the corresponding side on the other shape.
