Question

what scale factor would be applied to figure m to produce figure g? figure m (triangle) has side lengths 30, 24, 18. figure g (triangle) has side lengths 10, 8, 6.

Explanation:

Step1: Recall scale factor formula

The scale factor \( k \) from figure \( M \) to figure \( G \) is the ratio of corresponding side lengths, i.e., \( k=\frac{\text{Length of side in } G}{\text{Length of corresponding side in } M} \).

Step2: Choose a corresponding side pair

Let's take the vertical sides: in \( M \) it's \( 24 \), in \( G \) it's \( 8 \). So \( k = \frac{8}{24} \).

Step3: Simplify the fraction

Simplify \( \frac{8}{24} \) by dividing numerator and denominator by 8: \( \frac{8\div8}{24\div8}=\frac{1}{3} \). We can check with other sides: \( \frac{6}{18}=\frac{1}{3} \), \( \frac{10}{30}=\frac{1}{3} \), so the scale factor is consistent.

Answer:

\(\frac{1}{3}\)