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.
e. 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 scale factor from figure 1 to figure 3

Since figure 2 is a scale - drawing of figure 1 with a scale factor of \(1.7\), and figure 3 is a scale - drawing of figure 2 with a scale factor of \(0.6\).
The scale factor from figure 1 to figure 3 is the product of the two scale factors. Let \(k\) be the scale factor from figure 1 to figure 3. Then \(k = 1.7\times0.6\).

$$k=1.7\times0.6=(1 + 0.7)\times0.6=1\times0.6+0.7\times0.6=0.6 + 0.42 = 1.02$$

Step2: Determine if figure 3 is an enlargement or a reduction of figure 1

Since the scale factor \(k = 1.02>1\), figure 3 is an enlargement of figure 1.

Step3: Write the equation for part d

If \(y\) represents a side length of figure 3 and \(x\) represents the corresponding side length of figure 1, and the scale factor \(k = 1.02\), then the equation is \(y = 1.02x\)

Step4: Solve for part e

Given \(x = 8\) units and the equation \(y = 1.02x\). Substitute \(x = 8\) into the equation:

$$y=1.02\times8=(1+\frac{2}{100})\times8=1\times8+\frac{2}{100}\times8=8+\frac{16}{100}=8.16$$

Answer:

a. The scale factor is \(1.02\).
b. Figure 3 is an enlargement of figure 1.
d. The equation is \(y = 1.02x\).
e. The length of the corresponding side of figure 3 is \(8.16\) units.