The reflection of the line x = 3 over the line y = x would result in an image that is perpendicular to the given line. Option D) A reflection over the line y = x is the correct option.
To determine which transformation of the line x = 3 would result in an image that is perpendicular to the given line, let's consider each option:
A. A reflection over the line x = 1:
Reflecting the line x = 3 over the line x = 1 would not result in a perpendicular image. The reflected line would still be vertical and parallel to the original line.
B. A reflection over the y-axis:
Reflecting the line x = 3 over the y-axis would not result in a perpendicular image. The reflected line would still be vertical and parallel to the original line.
C. A reflection over the x-axis:
Reflecting the line x = 3 over the x-axis would not result in a perpendicular image. The reflected line would still be vertical and parallel to the original line.
D. A reflection over the line y = x:
Reflecting the line x = 3 over the line y = x would result in an image that is perpendicular to the given line. The reflected line would be horizontal and perpendicular to the original line.
Therefore, the transformation that would result in an image perpendicular to the given line is a reflection over the line y = x.
The image of the line graph is attached with the answer.