Question

the two figures are scaled copies of each other.
figure 1
figure 2
a. what is the scale factor that takes figure 1 to figure 2?
b. what is the scale factor that takes figure 2 to figure 1?

Explanation:

Step1: Select corresponding line - segments

Let's choose a line - segment in Figure 1 and its corresponding line - segment in Figure 2. For example, in Figure 1, if we consider the horizontal side of the triangle starting from point A. Suppose the length of a horizontal side of a triangle in Figure 1 is 2 units (counting the grid squares). The corresponding horizontal side of the similar - shaped triangle in Figure 2 is 4 units.

Step2: Calculate scale factor from Figure 1 to Figure 2

The scale factor $k_{12}$ from Figure 1 to Figure 2 is given by the ratio of the length of a side in Figure 2 to the length of the corresponding side in Figure 1. So, $k_{12}=\frac{\text{Length in Figure 2}}{\text{Length in Figure 1}}=\frac{4}{2} = 2$.

Step3: Calculate scale factor from Figure 2 to Figure 1

The scale factor $k_{21}$ from Figure 2 to Figure 1 is the reciprocal of the scale factor from Figure 1 to Figure 2. So, $k_{21}=\frac{\text{Length in Figure 1}}{\text{Length in Figure 2}}=\frac{2}{4}=\frac{1}{2}$.

Answer:

a. 2
b. $\frac{1}{2}$