reflect square ABCD with respect to the x-axis and the y-axis. what are the vertices of square A^!B^!C^!D^!
To reflect square ABCD with respect to the x-axis, you simply flip the square upside down. This means that the x-coordinates of each vertex will stay the same, but the y-coordinates will change sign.
So, if we have square ABCD with vertices A(1, 1), B(1, -1), C(-1, -1), and D(-1, 1), reflecting it with respect to the x-axis will give us square A'(1, -1), B'(1, 1), C'(-1, 1), and D'(-1, -1).
To reflect square ABCD with respect to the y-axis, you flip the square horizontally. This means that the y-coordinates of each vertex will stay the same, but the x-coordinates will change sign.
So, reflecting square ABCD with respect to the y-axis will give us square A''(-1, 1), B''(-1, -1), C''(1, -1), and D''(1, 1).
Therefore, the vertices of the reflected square A^!B^!C^!D^! are A^!(-1, -1), B^!(1, -1), C^!(1, 1), and D^!(-1, 1).