Which figure represents the image of parallelogram LMNP after a reflection across the line y = x?

To determine which figure represents the image of parallelogram LMNP after a reflection across the line y = x, we first need to understand what happens during this reflection. When a point (a, b) is reflected across the line y = x, its coordinates swap places, resulting in the new point (b, a).

Let’s break it down step by step:

1. Identify the coordinates of the vertices of the parallelogram LMNP.
2. Apply the reflection rule to each vertex:
• Vertex L(a1, b1) becomes L'(b1, a1)
• Vertex M(a2, b2) becomes M'(b2, a2)
• Vertex N(a3, b3) becomes N'(b3, a3)
• Vertex P(a4, b4) becomes P'(b4, a4)
3. Plot the new coordinates of the reflected vertices.
4. Finally, connect the dots to form the new parallelogram.

After performing these steps, we can then visually compare the resulting shape with the given figures to identify the correct one representing the reflected image of parallelogram LMNP.