Final answer:
To determine if two figures are similar, we compare their corresponding dimensions to see if they are proportional. The constant ratio is the scale factor, which describes the relationship between the dimensions of the figures. To determine the correct scale factor from given options, dimensions of the figures would be needed.
Step-by-step explanation:
Determining if Figures are Similar
To determine if two figures are similar and to find the scale factor, we compare their dimensions. For figures to be similar, their corresponding sides must be proportional. This means the ratio of a side of one figure to the corresponding side of the other figure must be constant. If this condition is met, the figures are similar and the constant ratio is the scale factor.
When you have a scale factor like 2:1, it tells you that every dimension on the scaled drawing is half the size of the actual object. Conversely, when converting actual dimensions to scale dimensions, you use the reciprocal of the scale factor.
For example, if the dimensions are given in different units, like inches to feet, you need to first convert them to the same units before comparing. Let's solve a problem using these concepts:
If a model's dimension is 4 inches and the scale factor is 1:2, then we set up a proportion to find the actual dimension, 1:2 = 4:x. Solving for x gives us the actual dimension.
The options presented in the question, such as 'scale factor 3:2', imply certain relationships between the dimensions of Figure A to Figure B. Only one of these options correctly represents the proportionate relationship that defines similarity. Without specific dimensions provided for the figures, we cannot determine which option correctly applies. Normally, such a determination would involve dividing one dimension by the corresponding dimension in the other figure.