Square ABCD

Question

𝐴
𝐵
𝐶
𝐷
has vertices A(2,4)
𝐴
(
2
,
4
)
, B(2,11)
𝐵
(
2
,
11
)
, C(7,11)
𝐶
(
7
,
11
)
, and D(7,4)
𝐷
(
7
,
4
)
. The square ABCD
𝐴
𝐵
𝐶
𝐷
is reflected on the x
𝑥
-axis and the y
𝑦
-axis. Find the coordinates of the vertices for square A′B′C′D′
𝐴
′
𝐵
′
𝐶
′
𝐷
′
. Choose 1 for Option A and 2 for Option B.

Option A: Square A′B′C′D′
𝐴
′
𝐵
′
𝐶
′
𝐷
′
has vertices A′(−2,−4)
𝐴
′
(
−
2
,
−
4
)
, B′(−2,−11)
𝐵
′
(
−
2
,
−
11
)
, C′(−7,−11)
𝐶
′
(
−
7
,
−
11
)
, and D′(−7,−4)
𝐷
′
(
−
7
,
−
4
)
.
Option B: Square A′B′C′D′
𝐴
′
𝐵
′
𝐶
′
𝐷
′
has vertices A′(2,−4)
𝐴
′
(
2
,
−
4
)
, B′(2,−11)
𝐵
′
(
2
,
−
11
)
, C′(7,−11)
𝐶
′
(
7
,
−
11
)
, and D′(7,−4)
𝐷
′
(
7
,
−
4
)
.(1 point)

Answer 1

To determine the correct coordinates after reflecting square ABCD on both the x-axis and the y-axis, we can perform the reflections step-by-step.

1. Reflection over the x-axis: This changes the y-coordinates of each vertex to their negative values, while the x-coordinates remain the same:

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

   This gives us the vertices A(2, -4), B(2, -11), C(7, -11), and D(7, -4).

2. Reflection over the y-axis: This changes the x-coordinates of each vertex to their negative values, while the y-coordinates stay the same:

   • 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 both reflections, the coordinates of the reflected square A'B'C'D' are:

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

These coordinates match the vertices listed in Option A.

Thus, the correct choice is Option A.