Final answer:
The scale factor of the dilation is (b) one-fourth, or a scale factor of 1:4.
Step-by-step explanation:
The scale factor in a dilation is a ratio that describes how much a figure has been increased or decreased in size. Given the choices provided, the answer is (b) One-fourth. When a figure undergoes dilation with a scale factor of 1:4, every dimension of the original figure is multiplied by 1/4 to find its corresponding dimension in the dilated figure.
Let's apply this concept with an example. If we have a scale dimension of 4, to find the actual dimension, we use the proportion given by:
1:2 = 4:x
Here, we cross-multiply to solve for x, which represents the actual dimension:
1 * x = 4 * 2
x = 8
Thus, the actual dimension is 8. This example illustrates how to use the scale factor and proportions to find missing dimensions in similar figures or drawings that have been scaled up or down.