Based on the given image, we need to determine the transformation rule that maps quadrilateral $ABCD$ to quadrilateral $LMNP$.

Observing the Reflection:

The quadrilateral $LMNP$ is a mirror image of $ABCD$ across the y-axis. This indicates that the x-coordinates of each vertex change signs while the y-coordinates remain unchanged.

Motion Rule:

The reflection rule is: $(x, y) \to (-x, y)$

Would you like further explanation or examples? Here are 5 follow-up questions for deeper exploration:

1. How do transformations like reflections differ from rotations?
2. What would the rule be for a reflection across the x-axis instead?
3. Can we combine transformations, such as reflection followed by translation?
4. How would you write a rule for reflecting over a line like $y = x$?
5. How can you verify the accuracy of a transformation rule using coordinates?

Tip: Always check one vertex from the pre-image and its corresponding vertex in the image to confirm the transformation rule.