Question

1. what is the scale factor that takes figure 1 to figure 2? 3. what is the scale factor that takes figure 2 to figure 1?

Explanation:

Step1: Select corresponding side lengths

Let's take side - length of a pair of corresponding sides. For example, if we consider the horizontal side of the smaller triangle (Figure 1) and the corresponding horizontal side of the larger triangle (Figure 2). Suppose the length of a horizontal side of Figure 1 is 2 units and the length of the corresponding horizontal side of Figure 2 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 \(k_1=\frac{\text{Side length of Figure 2}}{\text{Side length of Figure 1}}=\frac{4}{2} = 2\).

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 \(k_2=\frac{\text{Side length of Figure 1}}{\text{Side length of Figure 2}}=\frac{2}{4}=\frac{1}{2}\).

Answer:

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