To determine the coordinates of the image [tex]\( D^{\prime} \)[/tex] when point [tex]\( D \)[/tex] with coordinates [tex]\( (a, b) \)[/tex] is reflected over the line [tex]\( y = x \)[/tex], follow these steps:
1. Understand that reflecting a point over the line [tex]\( y = x \)[/tex] swaps its x-coordinate with its y-coordinate. Therefore,:
- The original coordinates of [tex]\( D \)[/tex] are [tex]\( (a, b) \)[/tex].
- After reflecting over the line [tex]\( y = x \)[/tex], the new coordinates [tex]\( D' \)[/tex] will be [tex]\( (b, a) \)[/tex].
Given this reflection rule, the coordinates of the image [tex]\( D^{\prime} \)[/tex] are [tex]\( (b, a) \)[/tex].
Thus, the correct answer is:
[tex]\[
(b, a)
\][/tex]
