the trapezoid fghi is a dilation of the trapezoid fghi. what is the scale factor of the dilation? simplify…

the trapezoid fghi is a dilation of the trapezoid 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.

the trapezoid fghi is a dilation of the trapezoid 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.

Answer

Explanation:

Step1: Select corresponding sides

Let's consider the vertical side of the trapezoids. For example, the vertical - side of trapezoid $FGHI$ from $G( - 2,8)$ to $H( - 2,4)$ has a length of $|8 - 4|=4$. The corresponding vertical - side of trapezoid $F'G'H'I'$ from $G'( - 2,4)$ to $H'( - 2,2)$ has a length of $|4 - 2| = 2$.

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 image to the length of the corresponding side of the pre - image. So, $k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}=\frac{2}{4}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$