Final answer:
The scale factor between two identical figures is 1, which means there is a 1:1 ratio in their dimensions with no change in size. An example of applying this is setting up and solving a proportion like 1:2 = 4:x, which results in the actual dimension being 8.
Step-by-step explanation:
When two figures are exactly the same, the scale factor from one to the other would be 1. This means that there is a 1:1 ratio in their dimensions, implying no change in size. To apply this concept, consider a proportion where you know one scale dimension and you wish to find the actual dimension. For example, if the given scale ratio is 1:2 and the scale dimension is 4, you would set up a proportion 1/2 = 4/x to find 'x', the actual dimension. Solving for 'x', you multiply both sides of the equation by 'x' and then both sides by 2 to isolate 'x', resulting in x = 2(4) or x = 8. Therefore, the actual dimension corresponding to a scale dimension of 4 when the ratio is 1:2 is 8.