Final answer:
Reflecting a square across the y-axis moves it from Quadrant III to Quadrant II, maintaining its size and shape while changing the sign of the x-coordinates of its points.
Step-by-step explanation:
When a square in Quadrant III with its sides aligned horizontally and vertically is reflected across the y-axis, the result is a square of the same size and shape located in Quadrant II. The reflection across the y-axis means that all points of the square will have their x-coordinates changed to the opposite sign, while the y-coordinates remain unchanged. Therefore, if the original square's lower left vertex was at the point (-x, -y) in Quadrant III, after reflection, its corresponding vertex will be at (x, -y) in Quadrant II, and similarly for the rest of the vertices. Consequently, the square's position will be horizontally mirrored onto the left side of the Cartesian coordinate system.