What figure represents the image of the parallelogram LMNP after reflecting it across the line y = x?

To determine the image of the parallelogram LMNP after reflection across the line y = x, we need to follow a systematic approach:

1. Understand the reflection process: When a point (x, y) is reflected across the line y = x, its coordinates are swapped. Therefore, the new coordinates become (y, x).
2. Identify the original vertices: Let’s suppose the coordinates of the vertices of parallelogram LMNP are as follows:
   • L (x₁, y₁)
   • M (x₂, y₂)
   • N (x₃, y₃)
   • P (x₄, y₄)
3. Apply the reflection formula: For each vertex, we will swap the coordinates as follows:
   • L’ (y₁, x₁)
   • M’ (y₂, x₂)
   • N’ (y₃, x₃)
   • P’ (y₄, x₄)
4. Plot the new vertices: Once we have the new coordinates, we can plot the vertices L’, M’, N’, and P’ on a Cartesian plane to visualize the new position of the parallelogram after the reflection.
5. Identify the final figure: The image of the parallelogram will retain its shape and area, but its orientation will change due to the reflection across y = x.

In conclusion, to find the figure that represents LMNP after the reflection across y = x, just remember to apply the coordinate swap to each vertex. You will then be able to accurately portray the reflected image of the parallelogram.