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).(1 point)
The square ABCD is reflected on the x-axis by changing the sign of the y-coordinates and on the y-axis by changing the sign of the x-coordinates.
For option A:
A'(-2, -4) - reflects the x-coordinate of A(2, 4) and the y-coordinate of A(2, 4)
B'(-2, -11) - reflects the x-coordinate of B(2, 11) and the y-coordinate of B(2, 11)
C'(-7, -11) - reflects the x-coordinate of C(7, 11) and the y-coordinate of C(7, 11)
D'(-7, -4) - reflects the x-coordinate of D(7, 4) and the y-coordinate of D(7, 4)
For option B:
A'(2, -4) - reflects the x-coordinate of A(2, 4)
B'(2, -11) - reflects the x-coordinate of B(2, 11)
C'(7, -11) - reflects the x-coordinate of C(7, 11)
D'(7, -4) - reflects the x-coordinate of D(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) which align with option A.
The correct answer is option A.