Question

proportions & scale factors quick check
a board game uses a triangular piece measuring 3 inches on each side. the travel version of the game uses a triangle in a proportional relationship to the original. it measures 0.5 inches on each side. identify the scale factor used to create the travel version of the piece. (1 point)
○ \\(\frac{1}{6}\\)
○ \\(-\frac{1}{6}\\)
○ 3.5
○ 6

Explanation:

Step1: Recall scale factor formula

The scale factor \( k \) is calculated as the ratio of the length of the new (travel version) side to the original side length. So \( k=\frac{\text{new length}}{\text{original length}} \).

Step2: Substitute values

Original side length is \( 3 \) inches, new (travel version) side length is \( 0.5 \) inches. Substitute into the formula: \( k = \frac{0.5}{3}=\frac{0.5\times2}{3\times2}=\frac{1}{6}\)? Wait, no, wait, 0.5 is \( \frac{1}{2} \), so \( \frac{\frac{1}{2}}{3}=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6} \)? Wait, no, wait the options have \( \frac{1}{6} \)? Wait the original is 3, travel is 0.5. So \( 0.5\div3=\frac{1}{2}\div3=\frac{1}{6} \)? Wait the options: first option is \( \frac{1}{6} \)? Wait the user's options: first option is \( \frac{1}{6} \)? Let me check again. Original length: 3 inches, travel length: 0.5 inches. Scale factor \( k=\frac{\text{travel length}}{\text{original length}}=\frac{0.5}{3}=\frac{1}{6} \). Wait, 0.5 is 1/2, so (1/2)/3 = 1/6. So the scale factor is \( \frac{1}{6} \).

Answer:

\(\frac{1}{6}\) (Assuming the first option is \(\frac{1}{6}\), so the answer is the option with \(\frac{1}{6}\), e.g., if the first option is A. \(\frac{1}{6}\), then A. \(\frac{1}{6}\))