the triangle abc is a dilation of the triangle abc. what is the scale factor of the dilation? simplify your…
the triangle abc is a dilation of the triangle abc. 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 side lengths
Let's consider the vertical side - length of the triangles. For $\triangle ABC$, the vertical side from $A$ to $C$ has a length of $2 - (- 2)=4$. For $\triangle A'B'C'$, the vertical side from $A'$ to $C'$ has a length of $6-(-6) = 12$.
Step2: Calculate the scale - factor
The scale factor $k$ of a dilation is given by the ratio of the lengths of corresponding sides of the dilated figure to the original figure. So, $k=\frac{\text{length of side in }A'B'C'}{\text{length of corresponding side in }ABC}$. Using the vertical sides we found above, $k = \frac{12}{4}=3$.
Answer:
3