Final answer:
The line of reflection that maps square ABCD onto itself, given the coordinates of its vertices, is y = 2. This line is the only option from the given list that passes through the midpoints of opposite sides of the square, making it symmetrical upon reflection.
Step-by-step explanation:
To determine which line of reflection would map square ABCD onto itself, we need to consider the coordinates of its vertices: C at (1,3), D at (1,1), A at (3,1), and B at (3,3). A line of reflection that would map this square onto itself would be one that divides the square into two symmetrical parts.
Observing the coordinates, we see that the square is symmetrical across a line that passes through the midpoints of opposite sides. The midpoints of sides AD and BC are both at x = 2 (the average of x-coordinates 1 and 3), and the midpoints of sides AB and CD are both at y = 2 (the average of y-coordinates 1 and 3).
Therefore, the lines of reflection that would map the square onto itself are x = 2 (a vertical line through these midpoints) and y = 2 (a horizontal line through these midpoints).
Looking at the provided options, we see that y = 2 is the correct choice as it is the only option that corresponds to a line passing through the midpoints of the sides of the square and hence reflects the square onto itself.