To find the foot of the perpendicular from the point (0, 0) to the line x + y = 2, we need to follow these steps:

Step 1: Find the slope of the given line.
The given equation of the line is x + y = 2. We can rewrite this equation in the slope-intercept form y = mx + c, where m is the slope of the line. Rearranging the equation, we get y = -x + 2. So, the slope of the line is -1.

Step 2: Find the equation of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. So, the slope of the line perpendicular to x + y = 2 is 1.

Step 3: Find the equation of the line passing through the point (0, 0) with slope 1.
Using the point-slope form of a line, we can write the equation of the line passing through (0, 0) with slope 1 as y - 0 = 1(x - 0), which simplifies to y = x.

Step 4: Find the point of intersection between the two lines.
To find the point of intersection between the lines y = -x + 2 and y = x, we can solve these equations simultaneously. Substituting y = x in the first equation, we get x = -x + 2. Solving this equation, we find x = 1. Substituting this value of x in either equation, we get y = 1.

Step 5: Find the foot of the perpendicular.
The foot of the perpendicular is the point of intersection between the line and the line perpendicular to it passing through the given point (0, 0). So, the foot of the perpendicular is (1, 1).

Therefore, the correct answer is option A, (1, 1).