Given Information:
- Two opposite vertices of a square: (-1,2) and (3,2)

Approach:
To find the coordinates of the other two vertices of the square, we need to understand the properties of a square. A square is a special type of quadrilateral with four equal sides and four right angles. The opposite sides of a square are parallel, and all four sides are equal in length.

Solution:

Step 1: Find the length of one side of the square.
To find the length of one side of the square, we can use the distance formula.
The distance formula is given by:
Distance = √((x2-x1)^2 + (y2-y1)^2)
Considering the given coordinates, we can calculate the distance between (-1,2) and (3,2) as follows:
Distance = √((3-(-1))^2 + (2-2)^2)
= √((3+1)^2 + 0^2)
= √(4^2)
= √16
= 4

Therefore, the length of one side of the square is 4 units.

Step 2: Find the coordinates of the other two vertices.
Since we know the length of one side of the square, we can use this information to find the coordinates of the other two vertices. Let's start with the given vertex (-1,2).

Vertex 1: (-1,2)
Since (-1,2) is one of the vertices, we can determine the coordinates of the other vertices by moving 4 units in different directions.

Vertex 2:
To find the coordinates of the second vertex, we need to move 4 units to the right from (-1,2).
Therefore, the coordinates of the second vertex are: (-1+4, 2) = (3, 2)

Vertex 3:
To find the coordinates of the third vertex, we need to move 4 units downwards from (-1,2).
Therefore, the coordinates of the third vertex are: (-1, 2-4) = (-1, -2)

Vertex 4:
To find the coordinates of the fourth vertex, we need to move 4 units to the left from (-1,2).
Therefore, the coordinates of the fourth vertex are: (-1-4, 2) = (-5, 2)

Conclusion:
The coordinates of the other two vertices of the square are (3,2) and (-1,-2).

It's not possible to solve it here for me