To determine the coordinates of the image \( D' \) after reflecting the point \( D(a, b) \) over the line \( y = x \), we need to understand the effect of this reflection on the point's coordinates.
When a point \( (x, y) \) is reflected over the line \( y = x \), its coordinates swap. That is, the x-coordinate and the y-coordinate trade places. So, the point \( (x, y) \) becomes \( (y, x) \).
Given the coordinates of point \( D \) are \( (a, b) \):
1. Start with the original coordinates of point \( D \): \( (a, b) \).
2. Reflect point \( D(a, b) \) over the line \( y = x \) by swapping the coordinates.
3. The new coordinates of the reflected point \( D' \) will thus be \( (b, a) \).
Therefore, the coordinates of the image \( D' \) are:
[tex]\[ (b, a) \][/tex]
Thus, the correct option is:
[tex]\[ (b, a) \][/tex]
