Question

the triangle stu is a dilation of the triangle stu. 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 corresponding side lengths

Let's consider the vertical side - length from \(T\) to \(S\) and from \(T'\) to \(S'\). The length of the segment \(TS\) is \(|- 6-(-10)| = 4\) units (using the \(y\) - coordinates of \(T\) and \(S\)). The length of the segment \(T'S'\) is \(|0 - (-2)|=2\) units (using the \(y\) - coordinates of \(T'\) and \(S'\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side in the image to the length of the corresponding side in the pre - image. So, \(k=\frac{\text{length of side in }S'T'U'}{\text{length of corresponding side in }STU}\). Substituting the values, we get \(k = \frac{2}{4}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)