Given:
- Line 2x-3y-4=0 is the perpendicular bisector of line AB.
- The co-ordinate of point A is (-3,1).

To find: The co-ordinate of point B.

Solution:
To find the co-ordinate of point B, we need to follow the below steps:
1. Find the equation of line AB.
2. Find the slope of line AB.
3. Find the slope of the perpendicular bisector of line AB.
4. Find the equation of the perpendicular bisector of line AB.
5. Find the point of intersection of the perpendicular bisector of line AB and the line AB.
6. Find the co-ordinate of point B.

Step 1: Find the equation of line AB.
Let's assume the co-ordinate of point B as (x,y).
So, the equation of line AB will be y - 1 = [(y - 1)/(x + 3)](x + 3 - (-3)) [Using point-slope form]
=> y - 1 = (y - 1)/(x + 3) * (x + 6)
=> (y - 1)(x + 3) = (y - 1)(x + 6)
=> x + 3 = x + 6
=> 3 = 6
This is not possible. So, line AB is a vertical line. And the co-ordinate of point B will be (-3, y) where y can be any real number.

Step 2: Find the slope of line AB.
The slope of a vertical line is undefined.

Step 3: Find the slope of the perpendicular bisector of line AB.
The slope of the perpendicular bisector of line AB will be the negative reciprocal of the slope of line AB.
As the slope of line AB is undefined, the slope of the perpendicular bisector of line AB will be 0.

Step 4: Find the equation of the perpendicular bisector of line AB.
The equation of the perpendicular bisector of line AB will be of the form y = mx + c where m is the slope and c is the y-intercept.
As the slope of the perpendicular bisector of line AB is 0, the equation of the perpendicular bisector of line AB will be y = c.

Step 5: Find the point of intersection of the perpendicular bisector of line AB and the line AB.
As the equation of the perpendicular bisector of line AB is y = c, it will intersect the line AB at (-3, c).

Step 6: Find the co-ordinate of point B.
From step 1, we know that the co-ordinate of point B is (-3, y).
From step 5, we know that the perpendicular bisector of line AB intersects line AB at (-3, c).
As the perpendicular bisector of line AB is the perpendicular bisector of line AB, the distance of point A from the perpendicular bisector of line AB will be equal to the distance of point B from the perpendicular bisector of line AB.
So, the distance between (-3,1) and (-3, c) will be equal to the distance between (-3, y) and (-