Final answer:
When you change which shape is the original, the scale factor becomes the reciprocal of the original scale factor. If A to B is 2:1, then B to A is 1:2. This concept is key for working with models, maps, and scaled representations.
Step-by-step explanation:
The relationship between scale factors when you change which shape is considered the original is that the scale factor is essentially the reciprocal of the original scale factor. If the scale factor from shape A to shape B is, for example, 2:1, this would suggest that shape B is twice as large as shape A. Conversely, if we consider shape B to be the original and want to determine the scale factor from B to A, we would take the reciprocal, yielding a scale factor of 1:2, indicating that shape A is half the size of shape B.
To apply this, if you're given a scale factor of A to B, such as 3:1, it means that A is 3 times as large as B. If you reverse this and want to find the scale factor from B to A, you would use the reciprocal, which would be 1:3, meaning B is one-third the size of A. This information is crucial in determining scale dimensions or actual dimensions when working with models, maps, or any other scaled representations.
In practical problems, such as if a rectangle has a width of 2 inches and a similar rectangle has a width of 9 inches, you could use the scale factor to determine how to convert between the two rectangles. In this case, the scale factor for converting the larger rectangle to the smaller rectangle is 2/9.