the triangle stu is a dilation of the triangle stu. what is the scale factor of the dilation? simplify your…

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.

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.

Answer

Explanation:

Step1: Select corresponding sides

Let's consider the vertical - side of the triangles. The length of the vertical side of $\triangle STU$ from $T(0, - 6)$ to $S(0,-10)$ is $|-6-(-10)| = 4$. The length of the vertical side of $\triangle S'T'U'$ from $T'(0,0)$ to $S'(0, - 2)$ is $|0 - (-2)|=2$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, $k=\frac{\text{length of side in }\triangle S'T'U'}{\text{length of side in }\triangle STU}=\frac{2}{4}$.

Step3: Simplify the ratio

Simplify $\frac{2}{4}$ to $\frac{1}{2}$.

Answer:

$\frac{1}{2}$