Question

the triangle vwx is a dilation of the triangle vwx. 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 vertices

First, identify coordinates of \( V, W, X \) and \( V', W', X' \).

• \( V(-2, 1) \), \( W(3, -2) \), \( X(-2, -3) \)
• \( V'(-6, 3) \), \( W'(9, -6) \), \( X'(-6, -9) \)

Step2: Calculate scale factor

Scale factor \( k \) is ratio of corresponding coordinates (e.g., \( x \)- or \( y \)-coordinate of image to pre - image).
For \( V \) to \( V' \): \( x \)-coordinate: \( \frac{-6}{-2}=3 \); \( y \)-coordinate: \( \frac{3}{1}=3 \).
Check with \( W \) to \( W' \): \( x \)-coordinate: \( \frac{9}{3}=3 \); \( y \)-coordinate: \( \frac{-6}{-2}=3 \).
Check with \( X \) to \( X' \): \( x \)-coordinate: \( \frac{-6}{-2}=3 \); \( y \)-coordinate: \( \frac{-9}{-3}=3 \).

Answer:

\( 3 \)