Question

the trapezoid klmn is a dilation of the trapezoid klmn. 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: Identify coordinates of a vertex

Take vertex \( K \) and \( K' \). Coordinates of \( K \): \( (-6, -6) \), coordinates of \( K' \): \( (-2, -2) \).

Step2: Calculate scale factor

Scale factor \( = \frac{\text{Coordinate of } K'}{\text{Coordinate of } K} \). For \( x \)-coordinate: \( \frac{-2}{-6} = \frac{1}{3} \). For \( y \)-coordinate: \( \frac{-2}{-6} = \frac{1}{3} \). So scale factor is \( \frac{1}{3} \).

Answer:

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