Question

triangle stv was dilated with the origin as the center of dilation to form \\( \triangle s ^ { \prime } t ^ { \prime } v ^ { \prime } \\).
what is the scale factor of the dilation?

Explanation:

Step1: Determine corresponding side lengths

Assume a side length of the smaller triangle (pre - image) and the larger triangle (image). For example, if we consider the horizontal segments from the center of dilation (origin) to a vertex. Let's say for the smaller triangle, a side length (distance from origin to a vertex) is \(2\) units, and for the larger triangle, it is \(6\) units.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of a side of the image}}{\text{length of the corresponding side of the pre - image}}\). Using the values from Step1: \(k = \frac{2}{6}=\frac{1}{3}\)

Answer:

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