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)

Answer 1

To determine the coordinates of the vertices A′B′C′D′ of square ABCD after being reflected on the x-axis and then the y-axis, we can apply the following transformations.

1. **Reflection across the x-axis**: The transformation changes the y-coordinates to their negatives.
- 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 are:
- A'(2, -4)
- B'(2, -11)
- C'(7, -11)
- D'(7, -4)

2. **Reflection across the y-axis**: The transformation changes the x-coordinates to their negatives.
- 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 are:
- A′′(-2, -4)
- B′′(-2, -11)
- C′′(-7, -11)
- D′′(-7, -4)

Thus, square A′B′C′D′ has vertices:

A′(-2, -4), B′(-2, -11), C′(-7, -11), D′(-7, -4).

This matches with Option A.

So the correct choice is **Option A:** Square A′B′C′D′ has vertices A′(−2,−4), B′(−2,−11), C′(−7,−11), and D′(−7,−4).