We are given two parallelograms, $ABCD$ and $EFGH$, where $EFGH$ is a dilation of $ABCD$. The dilation factor is the ratio between corresponding sides of the two parallelograms.

From the image:

• In parallelogram $ABCD$, side $AB$ = 4 units and side $AD$ = 2 units.
• In parallelogram $EFGH$, side $EF$ = 12 units and side $EH$ = 6 units.

To find the scale factor $k$, we compare the lengths of corresponding sides. Using side $AB$ and side $EF$: $k = \frac{EF}{AB} = \frac{12}{4} = 3.$ Thus, the scale factor $k = 3$.

The correct answer is $k = 3$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you determine corresponding sides in a dilation problem?
2. What happens to the angles during a dilation?
3. Can the scale factor in a dilation be negative?
4. How do you find the area of a figure after dilation?
5. How does dilation affect the perimeter of a figure?

Tip: Always verify the scale factor using multiple pairs of corresponding sides when possible to ensure accuracy.