Final answer:
The coordinates of the vertices of a square with side length b, centered at the origin, are (b/2, b/2), (b/2, -b/2), (-b/2, b/2), and (-b/2, -b/2), representing the four corners of the square.
Step-by-step explanation:
The question is asking for the coordinates of the vertices of a square centered at the origin, with side length b. To find these coordinates, we can consider the properties of a square: all sides are of equal length, and opposite sides are parallel. Since the square is centered at the origin and rotated such that its sides are parallel to the axes, half the side length will be the distance from the center to each vertex along the axes. Given that the side length is b, the coordinates of the vertices would be at a distance of b/2 from the origin along the x and y axes.
Hence, the coordinates of the vertices can be expressed as: (b/2, b/2), (b/2, -b/2), (-b/2, b/2), and (-b/2, -b/2). These points represent the top-right, bottom-right, top-left, and bottom-left vertices of the square, respectively.