Reflection of a Point in a Vertical Line:

When a point is reflected in a vertical line, the x-coordinate remains the same, but the y-coordinate changes its sign.

Given:
Point A = (-1, 5)
Line x = 1

To find the reflection of point A in the line x = 1, we need to determine the new coordinates of the reflected point.

Step 1: Visualize the Line and Point
Draw a graph with the line x = 1 and mark the point (-1, 5).

Step 2: Identify the Line of Reflection
The line x = 1 is a vertical line passing through the x-coordinate 1.

Step 3: Determine the Distance between the Point and the Line
The distance between the point (-1, 5) and the line x = 1 is 2 units (|1 - (-1)| = 2).

Step 4: Determine the Reflected Point
Since the line of reflection is vertical, the x-coordinate of the reflected point will remain the same as the original point (-1).

To find the y-coordinate of the reflected point, we need to change the sign of the original y-coordinate. In this case, the y-coordinate of the reflected point will be -5.

Therefore, the coordinates of the reflected point are (1, -5).

Step 5: Check the Options
Now let's check the given options to see which one matches the coordinates of the reflected point (1, -5).

a) (3, 5) - Incorrect
b) (5, 5) - Incorrect
c) (5, 3) - Incorrect
d) (3, -5) - Incorrect

Option A is the correct answer as it matches the coordinates of the reflected point (1, -5).

Conclusion:
The reflection of the point (-1, 5) in the line x = 1 is (1, -5).