What is reflected across the line y = x?

When a point is reflected across the line y = x, its coordinates are transformed in a specific way. For any point represented by the coordinates (a, b), this transformation swaps the x-coordinate and the y-coordinate. Thus, after reflection across the line y = x, the point (a, b) transforms into (b, a).

This is consistent with the geometric interpretation of the line y = x, which acts as a mirror. Any point on one side of this line will have its image on the opposite side, essentially switching its position concerning the line. This understanding solidifies why the answer indicating that the points (a, b) become (b, a) accurately captures the outcome of reflecting points across the line y = x.

In contrast, the other choices imply transformations that do not align with the true nature of this reflection. For instance, stating that the points remain unchanged does not apply since a reflection alters their positions relative to the axis. Similarly, transforming the coordinates to (-a, -b) represents a rotation or a reflection across the origin, which is not relevant to the line y = x. Lastly, suggesting the points become invariants implies that they do not change due to some property, which is incorrect