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).

Answer 1

To find the coordinates of the vertices of square ABCD after reflecting it over the x-axis and the y-axis, we first reflect the square over the x-axis and then over the y-axis.

1. Reflecting over the x-axis:

   • This changes the y-coordinate sign.
   • Coordinates after reflection:
     • A(2, 4) → A'(2, -4)
     • B(2, 11) → B'(2, -11)
     • C(7, 11) → C'(7, -11)
     • D(7, 4) → D'(7, -4)

   After this step, the coordinates are A'(2, -4), B'(2, -11), C'(7, -11), D'(7, -4).

2. Reflecting over the y-axis:

   • This changes the x-coordinate sign.
   • Coordinates after reflection:
     • A'(2, -4) → A''(-2, -4)
     • B'(2, -11) → B''(-2, -11)
     • C'(7, -11) → C''(-7, -11)
     • D'(7, -4) → D''(-7, -4)

   After this step, the coordinates are A''(-2, -4), B''(-2, -11), C''(-7, -11), and D''(-7, -4).

Thus, the final coordinates of the vertices after both reflections are:

• A''(-2, -4), B''(-2, -11), C''(-7, -11), D''(-7, -4).

Comparing with the options:

• 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 correct answer is Option A.