To solve the problem of finding the coordinates of the reflected point \( D^{\prime} \) when reflecting point \( D(a, b) \) over the line \( y = x \), let's follow these steps:
1. Understanding the Reflection over \( y = x \):
When reflecting a point over the line \( y = x \), the coordinates of the point are swapped. This means that if \( D \) has coordinates \( (a, b) \), the coordinates of its reflection over the line \( y = x \) will be \( (b, a) \).
2. Reflection Process:
- The original point \( D \) is given as \( (a, b) \).
- The reflection of point \( (a, b) \) over the line \( y = x \) involves swapping the \( x \) and \( y \) coordinates.
3. Finding the Coordinates of \( D^{\prime} \):
- After swapping the coordinates of point \( D(a, b) \), the new coordinates will be \( (b, a) \).
Therefore, the coordinates of the image \( D^{\prime} \) after reflecting point \( D \) over the line \( y = x \) are \( (b, a) \).
So, the answer is:
[tex]\[ \boxed{(b, a)} \][/tex]
