Question

the trapezoid vwxy is a dilation of the trapezoid vwxy. 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: Select corresponding sides

Choose the horizontal - top sides of the trapezoids. The length of the top - side of trapezoid $VWXY$ (segment $YX$) is from $x=-2$ to $x = 2$, so $YX=4$. The length of the top - side of trapezoid $V'W'X'Y'$ (segment $Y'X'$) is from $x=-6$ to $x = 8$, so $Y'X' = 14$.

Step2: Calculate 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 $k=\frac{Y'X'}{YX}$. Substitute $Y'X' = 14$ and $YX = 4$ into the formula: $k=\frac{14}{4}=\frac{7}{2}$.

Answer:

$\frac{7}{2}$