Determining the reflection of a point across the line y = x results in which transformation?

When reflecting a point across the line ( y = x ), the coordinates of the point undergo a specific transformation. The line ( y = x ) acts as a mirror, meaning that for any point represented as ( (x, y) ), swapping its coordinates will produce the reflection.

In this case, if the original point is ( (x, y) ), the reflection across the line ( y = x ) will result in the point ( (y, x) ). This shift effectively means that the x-coordinate of the original point becomes the y-coordinate of the new point and vice versa.

Thus, the correct transformation that describes this reflection is represented as ( (x, y) = (y, x) ). This demonstrates how the coordinates are interchanged during the reflection process.