Question

b. what is the scale factor that takes figure 1 to figure 2?
c. what is the scale factor that takes figure 2 to figure 1?

Explanation:

Step1: Select corresponding side lengths

Let's consider side \(AC\) in Figure 1 and side \(PR\) in Figure 2. Assume the length of \(AC\) is \(2\) units (by counting grid - squares) and the length of \(PR\) is \(4\) units.

Step2: Calculate scale factor from Figure 1 to Figure 2

The scale factor \(k_1\) from Figure 1 to Figure 2 is given by the ratio of the side - length of Figure 2 to the side - length of Figure 1. So \(k_1=\frac{\text{length in Figure 2}}{\text{length in Figure 1}}=\frac{4}{2} = 2\).

Step3: Calculate scale factor from Figure 2 to Figure 1

The scale factor \(k_2\) from Figure 2 to Figure 1 is the reciprocal of the scale factor from Figure 1 to Figure 2. So \(k_2=\frac{\text{length in Figure 1}}{\text{length in Figure 2}}=\frac{2}{4}=\frac{1}{2}\).

Answer:

b. The scale factor that takes Figure 1 to Figure 2 is \(2\).
c. The scale factor that takes Figure 2 to Figure 1 is \(\frac{1}{2}\).