Question

Question
Square ABCD
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 reflect the square ABCD across the x-axis and then the y-axis, we will perform the following transformations:

1. **Reflection over the x-axis**: This changes the y-coordinate of each vertex to its negative.
- A(2, 4) → A'(2, -4)
- B(2, 11) → B'(2, -11)
- C(7, 11) → C'(7, -11)
- D(7, 4) → D'(7, -4)

2. **Reflection over the y-axis**: This changes the x-coordinate of each vertex to its negative.
- 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 vertices of square A''B''C''D'' are:
- A''(-2, -4)
- B''(-2, -11)
- C''(-7, -11)
- D''(-7, -4)

Thus, the correct option is:

**Option A**: Square A'B'C'D' has vertices A'(-2, -4), B'(-2, -11), C'(-7, -11), and D'(-7, -4).

So, you would choose **1 for Option A**.