Square ABCD has vertices A(2,4), B(2,11), C(7,11), and D(7,4). The square ABCD is reflected on the x-axis and the y-axis. Find the coordinates of the vertices for square A′B′C′D′. Choose 1 for Option A and 2 for Option B.
Option A: Square A′B′C′D′ has vertices A′(−2,−4), B′(−2,−11), C′(−7,−11), and D′(−7,−4).
Option B: Square A′B′C′D′ has vertices A′(2,−4), B′(2,−11), C′(7,−11), and D′(7,−4).
The x-axis reflection of a point (x, y) gives us a new point (-x, y). The y-axis reflection of a point (x, y) gives us a new point (x, -y).
Applying the x-axis reflection to the vertices of square ABCD:
Vertex A: (2, 4) => (-2, 4)
Vertex B: (2, 11) => (-2, 11)
Vertex C: (7, 11) => (-7, 11)
Vertex D: (7, 4) => (-7, 4)
Applying the y-axis reflection to the new vertices:
Vertex A': (-2, 4) => (-2, -4)
Vertex B': (-2, 11) => (-2, -11)
Vertex C': (-7, 11) => (-7, -11)
Vertex D': (-7, 4) => (-7, -4)
Therefore, the coordinates of the vertices for square A'B'C'D' are A'(-2, -4), B'(-2, -11), C'(-7, -11), and D'(-7, -4).
The correct answer is Option A: Square A′B′C′D′ has vertices A′(−2,−4), B′(−2,−11), C′(−7,−11), and D′(−7,−4).