Question

point b is the center of dilation. what is the scale factor?

Explanation:

Step1: Measure corresponding side lengths

Let's assume we measure a side - length of the original figure (pre - image) and the corresponding side - length of the dilated figure (image). Suppose a side of figure $A$ has a length of 4 units and the corresponding side of figure $A'$ has a length of 2 units.

Step2: Calculate scale factor formula

The scale factor $k$ is given by the formula $k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}$. So, $k = \frac{2}{4}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$