Final answer:
The type of dilation and scale factor depend on whether the scale factor is less than or greater than 1. Examples demonstrate how scale factor ratios are used to proportionally increase or decrease dimensions in scaled drawings or models.
Step-by-step explanation:
Without the exact details of the transformation from A to B, we must make use of the provided information to deduce the type of dilation (reduction or enlargement) and the scale factor. A scale factor less than 1 indicates a reduction, while a scale factor greater than 1 indicates an enlargement. The scale factor is a ratio that describes how the size of an object is increased or decreased.
Let's examine one of the provided examples to understand how scale factors work:
- If you have a scale factor of 1:4, and the scale measurement is 4, to find the actual dimension you would set up a proportion like 1:2 = 4:x, solving for x.
- In this case, since a 1:4 ratio is being used, every measurement of the actual object is 4 times larger than the scale measurement, indicating a reduction when going from actual size to scale size.
Similarly, if an actual man is 64 inches tall and a drawing represents him at 4 inches tall, the scale factor for the drawing is 1:16, because 4 inches is 1/16th of 64 inches, which also indicates a reduction.