To reflect a point over the line [tex]\( y = x \)[/tex], you need to swap the coordinates of the point.
Given the coordinates of point [tex]\( D \)[/tex] as [tex]\( (a, b) \)[/tex]:
1. Reflecting over the line [tex]\( y = x \)[/tex] involves swapping the [tex]\( x \)[/tex]-coordinate with the [tex]\( y \)[/tex]-coordinate.
2. Therefore, for point [tex]\( D \)[/tex] with coordinates [tex]\( (a, b) \)[/tex], the reflected image [tex]\( D' \)[/tex] will have its coordinates swapped to [tex]\( (b, a) \)[/tex].
So, the coordinates of the image [tex]\( D' \)[/tex] after reflecting point [tex]\( D \)[/tex] over the line [tex]\( y = x \)[/tex] are [tex]\( (b, a) \)[/tex].
Thus, the correct answer is:
[tex]\[ (b, a) \][/tex]
