Let's consider the given information:
- The square has an area of 36 square units.
- One side of the square lies along the line y = 3.
Since the area of a square is equal to the side length squared, we can find the side length of the square first. Let's call the side length "s."
Area of the square = s^2 = 36
Taking the square root of both sides:
s = √36
s = 6
Now that we know the side length of the square is 6 units, and one side lies along the line y = 3, we can determine the possible location of one of the vertices.
If one side of the square lies along the line y = 3, that means one of the vertices is located at (x, 3), where "x" is a coordinate on the x-axis. Since the square is symmetric, the other vertices would have the same y-coordinate of 3.
So, one of the vertices of the square could be located at (x, 3). The x-coordinate can be any value since the square can be positioned at different locations along the line y = 3. Therefore, the location of one of the vertices of the square is (x, 3), where "x" can be any real number.