To solve this problem, we need to understand how coordinates change under reflection over the line [tex]\( y = x \)[/tex].
When a point [tex]\( (a, b) \)[/tex] is reflected over the line [tex]\( y = x \)[/tex], the coordinates of the reflected point are obtained by swapping the x-coordinate and y-coordinate of the original point.
Therefore, if the original point [tex]\( D \)[/tex] has coordinates [tex]\( (a, b) \)[/tex], after reflecting it over the line [tex]\( y = x \)[/tex], the new coordinates of the image will be [tex]\( (b, a) \)[/tex].
Given the options:
1. [tex]\((a, -b)\)[/tex]
2. [tex]\((b, a)\)[/tex]
3. [tex]\((-a, b)\)[/tex]
4. [tex]\((-b, -a)\)[/tex]
The correct coordinates of the image of point [tex]\( D \)[/tex] after the reflection over the line [tex]\( y = x \)[/tex] are [tex]\((b, a)\)[/tex].
Thus, the coordinates of the image of point [tex]\( D \)[/tex] are [tex]\( \boxed{(b, a)} \)[/tex].
