If point D with coordinates (a,b) is reflected over the line y=x then the image point D' coordinates are (b,a) (see picture for details).
The middlepoint M of segment DD' lhas coordinates and lies on the line y=x (since its coordinates are equal), DD' is perpendicular to the line y=x and DM=D'M. All these remarks show that the point D' is the image point of D.
