When reflecting a point [tex]\((a, b)\)[/tex] over the line [tex]\(y = x\)[/tex], you swap the [tex]\(x\)[/tex]- and [tex]\(y\)[/tex]-coordinates of the point. This means the [tex]\(x\)[/tex]-coordinate of the image will be [tex]\(b\)[/tex] and the [tex]\(y\)[/tex]-coordinate of the image will be [tex]\(a\)[/tex].
Given the coordinates of point [tex]\(D\)[/tex] as [tex]\((a, b)\)[/tex], the steps to find the coordinates of the reflected image [tex]\(D'\)[/tex] are as follows:
1. Start with the coordinates of the original point [tex]\(D\)[/tex], which are [tex]\((a, b)\)[/tex].
2. Reflect the point over the line [tex]\(y = x\)[/tex]; to do this, you swap the [tex]\(x\)[/tex]-coordinate and [tex]\(y\)[/tex]-coordinate.
3. After swapping, the new coordinates are [tex]\((b, a)\)[/tex].
Thus, the coordinates of the image point [tex]\(D'\)[/tex] after reflecting [tex]\(D(a, b)\)[/tex] over the line [tex]\(y = x\)[/tex] are [tex]\((b, a)\)[/tex].
Therefore, the correct answer is [tex]\((b, a)\)[/tex].
