Question

the parallelogram jklm is a dilation of the parallelogram jklm. 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

Let's consider the horizontal - side lengths of the parallelograms. The length of side $JK$ in parallelogram $JKLM$: The $x$ - coordinates of $J(-2,4)$ and $K(6,4)$ are used. The length of $JK=\vert6 - (-2)\vert=8$. The length of side $J'K'$ in parallelogram $J'K'L'M'$: The $x$ - coordinates of $J'(-1,2)$ and $K'(3,2)$ are used. The length of $J'K'=\vert3-(-1)\vert = 4$.

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, $k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}=\frac{J'K'}{JK}=\frac{4}{8}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$