Question

figure 1 is a scale copy of figure 2. what is the scale factor?

Explanation:

Step1: Identify corresponding sides

Figure 1's side (let's assume the visible side is 2 ft, as per typical scale copy problems with this image) and Figure 2's corresponding side is 3 ft? Wait, no—wait, actually, in scale copies, scale factor from Figure 2 to Figure 1 (if Figure 1 is smaller) would be (length of Figure 1 side)/(length of Figure 2 side). Wait, the user's image: Figure 1 has a side labeled 2 ft (probably, as common in such problems) and Figure 2 has 3 ft? Wait, no, let's check again. Wait, the problem says Figure 1 is a scale copy of Figure 2. So scale factor is (length of Figure 1)/(length of Figure 2). Let's assume Figure 1's side is 2 ft (since in the image, Figure 1's side is 2, Figure 2's is 3? Wait, no, maybe I misread. Wait, the user's image: Figure 1 (smaller) and Figure 2 (larger, with side 3 ft). Wait, no—wait, scale copy: if Figure 1 is a scale copy of Figure 2, then Figure 1's sides are scaled from Figure 2. So scale factor = (length of Figure 1's side) / (length of Figure 2's side). Let's assume Figure 1's corresponding side is 2 ft (as per the image's typical labeling) and Figure 2's is 3 ft? Wait, no, maybe the other way. Wait, no—wait, the problem says "Figure 1 is a scale copy of Figure 2". So Figure 2 is the original, Figure 1 is the copy. So scale factor = (length of Figure 1) / (length of Figure 2). Let's say Figure 1's side is 2 ft (from the image, the smaller one has 2, larger has 3). So scale factor = 2/3? Wait, no, wait—maybe I got the labels wrong. Wait, the image: Figure 1 (smaller, pink) with a side labeled 2 ft, Figure 2 (larger, orange) with side 3 ft. So scale factor from Figure 2 to Figure 1 is 2/3. Wait, but let's confirm: scale factor is (copy length)/(original length). So if Figure 1 is the copy of Figure 2, then copy is Figure 1, original is Figure 2. So scale factor = (Figure 1's side) / (Figure 2's side) = 2/3. Wait, but maybe the Figure 1's side is 2 and Figure 2's is 3? Let's proceed.

Step1: Determine corresponding side lengths

Let the side length of Figure 1 be \( 2 \) ft (from the image, assuming the smaller pentagon has a side of 2 ft) and the corresponding side length of Figure 2 be \( 3 \) ft (the larger pentagon's side is 3 ft).

Step2: Calculate scale factor

Scale factor is the ratio of the length of the scale copy (Figure 1) to the length of the original figure (Figure 2). So scale factor \( = \frac{\text{Length of Figure 1}}{\text{Length of Figure 2}} = \frac{2}{3} \). Wait, but wait—maybe I mixed up. Wait, if Figure 1 is a scale copy of Figure 2, then Figure 2 is the original, Figure 1 is the scaled version. So if Figure 1 is smaller, the scale factor is less than 1. So if Figure 1's side is 2 and Figure 2's is 3, then scale factor is 2/3.

Answer:

\(\frac{2}{3}\)