Question

the parallelogram opqr is a dilation of the parallelogram opqr. 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 side lengths

Let's consider the horizontal side lengths of the parallelograms. The length of side $OP$ in parallelogram $OPQR$ can be found by calculating the difference in $x -$ coordinates of $O(- 2,-4)$ and $P(2,-4)$. So, $OP=\vert2 - (-2)\vert=4$. The length of side $O'P'$ in parallelogram $O'P'Q'R'$ with $O'(-8,-10)$ and $P'(8,-10)$ is $O'P'=\vert8-(-8)\vert = 16$.

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, $k=\frac{O'P'}{OP}$. Substituting the values we found, $k = \frac{16}{4}=4$.

Answer:

$4$