Question

d. write an equation that could be used to find any side length of figure 3 given a corresponding side length of figure 1. let y represent a side length of figure 3, and let x represent the corresponding side length of figure 1
c. if the length of a side of figure 1 is 8 units, what is the length of the corresponding side of figure 3?

1. figure 2 is a scale drawing of figure 1 and is produced with a scale factor of 1.7. figure 3 is a scale drawing of figure 2 and is produced with a scale factor of 0.6.

a. what scale factor is used to relate the side lengths of figure 1 to the side lengths of figure 3?
b. is figure 3 an enlargement or a reduction of figure 1?

Explanation:

Step1: Find the overall scale factor

Since Figure 2 has a scale factor of \(1.7\) from Figure 1 and Figure 3 has a scale factor of \(0.6\) from Figure 2. The overall scale factor from Figure 1 to Figure 3 is the product of the two scale factors.

$$y = 1.7\times0.6x$$

$$y = 1.02x$$

Step2: Determine if it is an enlargement or reduction

Since the scale factor \(1.02> 1\), when the scale factor \(k>1\), the new figure (Figure 3) is an enlargement of the original figure (Figure 1)

Step3: Calculate the side - length of Figure 3 when \(x = 8\)

Substitute \(x = 8\) into the equation \(y=1.02x\)

$$y=1.02\times8$$

$$y = 8.16$$

Answer:

a. The scale factor is \(1.02\)
b. Figure 3 is an enlargement of Figure 1
c. The length of the corresponding side of Figure 3 is \(8.16\) units