Question

Question
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)
.(1 point)
Remaining Attempts : 3

Answer 1

To find the coordinates of the vertices of square \( A'B'C'D' \) after reflecting square \( ABCD \) on the x-axis and the y-axis, we will apply the reflections step-by-step.

1. **Reflecting over the x-axis:**
- The reflection of a point \( (x, y) \) over the x-axis is given by \( (x, -y) \).
- Applying this to the vertices of square \( ABCD \):
- \( A(2, 4) \) becomes \( A'(2, -4) \)
- \( B(2, 11) \) becomes \( B'(2, -11) \)
- \( C(7, 11) \) becomes \( C'(7, -11) \)
- \( D(7, 4) \) becomes \( D'(7, -4) \)

After this reflection, the coordinates of the vertices are:
- \( A'(2, -4) \)
- \( B'(2, -11) \)
- \( C'(7, -11) \)
- \( D'(7, -4) \)

2. **Reflecting over the y-axis:**
- The reflection of a point \( (x, y) \) over the y-axis is given by \( (-x, y) \).
- Applying this to the vertices after the first reflection:
- \( A'(2, -4) \) becomes \( A''(-2, -4) \)
- \( B'(2, -11) \) becomes \( B''(-2, -11) \)
- \( C'(7, -11) \) becomes \( C''(-7, -11) \)
- \( D'(7, -4) \) becomes \( D''(-7, -4) \)

After both reflections, the final vertices of square \( A'B'C'D' \) are:
- \( A''(-2, -4) \)
- \( B''(-2, -11) \)
- \( C''(-7, -11) \)
- \( D''(-7, -4) \)

Now we compare this with the provided options:

**Option A:**
- \( A'(-2, -4) \)
- \( B'(-2, -11) \)
- \( C'(-7, -11) \)
- \( D'(-7, -4) \)

**Option B:**
- \( A'(2, -4) \)
- \( B'(2, -11) \)
- \( C'(7, -11) \)
- \( D'(7, -4) \)

The correct option corresponds to Option A.

Thus, the answer is **1 (Option A)**.