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)
what is A

Answer 1

To find the coordinates of the vertices for square A′B′C′D′ after reflecting it on the x-axis and then on the y-axis, we can perform the transformations based on the original coordinates of square ABCD.

1. Original vertices:

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

2. Reflection over the x-axis:

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

3. Reflection over the y-axis:

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

Thus, after reflecting square ABCD over both axes, 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).

So, comparing with the options given:

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 choice is Option A.