Question

the triangle lmn is a dilation of the triangle lmn. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find coordinates of original and dilated points

Original points: \( L(-10, 0) \), \( M(0, -10) \), \( N(-10, 10) \)
Dilated points: \( L'(-2, 0) \), \( M'(0, -2) \), \( N'(-2, 2) \)

Step2: Calculate scale factor (ratio of corresponding lengths)

Take \( L \) to \( L' \): \( \frac{\text{Length of } L'M'N'}{\text{Length of } LMN} = \frac{\text{Distance from } L' \text{ to origin}}{\text{Distance from } L \text{ to origin}} \)
Distance \( L \) to origin: \( \sqrt{(-10 - 0)^2 + (0 - 0)^2} = 10 \)
Distance \( L' \) to origin: \( \sqrt{(-2 - 0)^2 + (0 - 0)^2} = 2 \)
Scale factor \( = \frac{2}{10} = \frac{1}{5} \)

Answer:

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