Question

the rectangle fghi is a dilation of the rectangle fghi. 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: Choose a corresponding side

Let's consider the vertical side of the rectangles. The length of side $IH$ in rectangle $FGHI$ is from $y = 2$ to $y = 4$, so $IH=4 - 2=2$. The length of side $I'H'$ in rectangle $F'G'H'I'$ is from $y = 4$ to $y = 8$, so $I'H'=8 - 4 = 4$.

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 dilated figure to the length of the corresponding side in the original figure. So $k=\frac{I'H'}{IH}$. Substituting the values we found, $k = \frac{4}{2}=2$.

Answer:

$2$