What is the result of a reflection over the line y=x?

When reflecting a point over the line ( y = x ), the result is that the coordinates of the point are swapped. For a given point ( (a, b) ), reflecting it over the line ( y = x ) will yield the new coordinates ( (b, a) ). This means that the x-coordinate becomes the y-coordinate and vice versa. Thus, the transformation involves switching the positions of the x and y coordinates, which is why the choice indicating this swap is the correct answer.

Reflection in this manner preserves the distances from the line ( y=x ), maintaining the geometric properties of the point while changing its location. The other options do not accurately describe this process; they involve operations that do not relate directly to the concept of reflection. For instance, changing the sign of the x-coordinate or multiplying the coordinates by a scale factor does not represent what happens during reflection over the line ( y=x ).