Ask a New Question
Menu

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)
which A?

2 answers

To find the vertices of square \( A'B'C'D' \) after reflecting square \( ABCD \) across the x-axis and then the y-axis, we will perform each reflection step-by-step.

  1. Reflection across 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)

    After reflecting across the x-axis, the coordinates of the vertices are:

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

  2. Reflection across 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)

After reflecting across the y-axis, the final coordinates of the vertices are:

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

Comparing this with the provided options:

  • Option A: Square \( A'B'C'D' \) has vertices A'(-2, -4), B'(-2, -11), C'(-7, -11), and D'(-7, -4). (This is correct)

  • Option B: Square \( A'B'C'D' \) has vertices A'(2, -4), B'(2, -11), C'(7, -11), and D'(7, -4). (This is incorrect)

Thus, the correct option is Option A.

what is A