Question

question 10 of 10
what is the scale factor from $\triangle abc$ to $\triangle xyz$
image of two triangles, $\triangle abc$ with sides 45, 35, 60 and angles 98°, 35°, 48°; $\triangle xyz$ with sides 9, 7, 12 and angles 98°, 35°, 48°
a. $\frac{1}{5}$
b. 3
c. 5
d. $\frac{1}{3}$

Explanation:

Step1: Identify Corresponding Sides

In similar triangles \( \triangle ABC \) and \( \triangle XYZ \), find corresponding sides. For example, side \( AB = 45 \) in \( \triangle ABC \) and side \( XY = 9 \) in \( \triangle XYZ \).

Step2: Calculate Scale Factor

Scale factor from \( \triangle ABC \) to \( \triangle XYZ \) is \( \frac{\text{Length of side in } \triangle XYZ}{\text{Length of corresponding side in } \triangle ABC} \). So, \( \frac{9}{45}=\frac{1}{5} \)? Wait, no, wait. Wait, maybe I mixed up. Wait, scale factor from \( ABC \) to \( XYZ \) is \( \frac{XYZ \text{ side}}{ABC \text{ side}} \). Let's check another side. \( BC = 60 \), \( YZ = 12 \). Then \( \frac{12}{60}=\frac{1}{5} \)? Wait, no, wait \( AB = 45 \), \( XY = 9 \). \( 9/45 = 1/5 \). \( AC = 35 \), \( XZ = 7 \). \( 7/35 = 1/5 \). So the scale factor is \( \frac{1}{5} \)? Wait, no, wait the options: A is \( 1/5 \), D is \( 1/3 \). Wait, let's recalculate. Wait, maybe I got the direction wrong. Wait, scale factor from \( ABC \) to \( XYZ \): \( XYZ \) is smaller, so the scale factor is \( \frac{\text{XYZ side}}{\text{ABC side}} \). So \( XY = 9 \), \( AB = 45 \). \( 9/45 = 1/5 \). So that's correct. So the scale factor is \( 1/5 \), which is option A. Wait, but let me check again. \( AB = 45 \), \( XY = 9 \). \( 9 \div 45 = 1/5 \). \( AC = 35 \), \( XZ = 7 \). \( 7 \div 35 = 1/5 \). \( BC = 60 \), \( YZ = 12 \). \( 12 \div 60 = 1/5 \). So yes, the scale factor is \( 1/5 \), so option A.

Answer:

A. \( \frac{1}{5} \)