Given:
We are given two points on a line: (a, b) and (-a, -b).

To find:
We need to determine which of the given points lie on the line passing through the given points.

Solution:
Let's find the equation of the line passing through the points (a, b) and (-a, -b).

Step 1: Finding the slope of the line
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Using this formula, we can find the slope of the line passing through (a, b) and (-a, -b):

m = (-b - b) / (-a - a)
m = -2b / -2a
m = b / a

Step 2: Finding the equation of the line
We know that the equation of a line in slope-intercept form is given by y = mx + c, where m is the slope and c is the y-intercept.

Since we have the slope (b / a), we can substitute it into the equation:

y = (b / a) * x + c

Now, let's substitute one of the given points to find the value of c.

Using the point (a, b):
b = (b / a) * a + c
b = b + c

Therefore, c = 0.

So, the equation of the line passing through the points (a, b) and (-a, -b) is:
y = (b / a) * x

Step 3: Checking the options
Now, let's substitute the coordinates of each option into the equation of the line and see which one satisfies it.

a) (1, 1):
1 = (b / a) * 1
1 = b / a
This option does not satisfy the equation.

b) (a^2, ab):
ab = (b / a) * a^2
ab = b * a
This option satisfies the equation.

c) (3a, -2b):
-2b = (b / a) * 3a
-2b = 3b
This option does not satisfy the equation.

d) None of these

Therefore, the correct answer is option B, (a^2, ab), as it satisfies the equation of the line passing through the given points.