Question

question 3 of 10

what is the scale factor from \\(\delta abc\\) to \\(\delta def\\)?

a. \\(\frac{1}{2}\\)
b. 3
c. 2
d. \\(\frac{1}{3}\\)

Explanation:

Identify corresponding sides

Using the Triangle Similarity knowledge point, we identify corresponding sides of similar triangles \(\Delta ABC\) and \(\Delta DEF\).
Corresponding pairs:

• \(AB\) corresponds to \(DE\)
• \(BC\) corresponds to \(EF\)
• \(AC\) corresponds to \(DF\)

Retrieve side lengths

Using the Triangle Similarity knowledge point, we find the lengths of corresponding sides from the given figures:

• \(AB = 5\), \(DE = 15\)
• \(BC = 4\), \(EF = 12\)
• \(AC = 3\), \(DF = 9\)

Calculate the scale factor

Using the Triangle Similarity knowledge point, the scale factor \(k\) from \(\Delta ABC\) to \(\Delta DEF\) is the ratio of any side length in the image triangle to its corresponding side length in the pre-image triangle:

$$ k = \frac{DE}{AB} = \frac{15}{5} = 3 $$

$$ k = \frac{EF}{BC} = \frac{12}{4} = 3 $$

$$ k = \frac{DF}{AC} = \frac{9}{3} = 3 $$

The scale factor is \(3\).

Answer:

• A. \(\frac{1}{2}\)
• B. 3 (Correct answer)
• C. 2
• D. \(\frac{1}{3}\)