Question

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 9 to 9 in one unit increments. The y-axis ranges from negative 11 to 11 in one unit increments. Four points are plotted. A square is graphed using the four plotted points as vertices. Point A is plotted at coordinates left parenthesis 3 comma negative 4 right parenthesis. Point B is plotted at coordinates left parenthesis 7 comma negative 4 right parenthesis. Point C is plotted at coordinates left parenthesis 7 comma negative 8 right parenthesis. Point D is plotted at coordinates left parenthesis 3 comma negative 8 right parenthesis. Points A, B, C, and D are connected by solid lines to form square A B C D.

reflect square abcd first across the x-axis, and then across the y-axis to create square a'b'c'd' what are the vertices of square a'b'c'd'?


Square A′B′C′D′
has vertices A′(−3,−4)
, B′(−7,−4)
, C′(−7,−8)
, and D′(−3,−8)
.

Square A′B′C′D′
has vertices A′(−3,4)
, B′(−7,4)
, C′(−7,8)
, and D′(−3,8)
.

Square A′B′C′D′
has vertices A′(−3,4)
, B′(−7,4)
, and C′(−7,8)
.

Square A′B′C′D′
has vertices A′(3,4)
, B′(7,4)
, C′(7,8)
, and D′(3,8)
.

Answer 1

To find the vertices of square A'B'C'D' after reflecting square ABCD across the x-axis and then the y-axis, let's follow the steps:

1. **Vertices of Square ABCD**:
- A(3, -4)
- B(7, -4)
- C(7, -8)
- D(3, -8)

2. **Reflect across the x-axis**:
When a point (x, y) is reflected across the x-axis, the new point becomes (x, -y):
- A'(3, -(-4)) → A'(3, 4)
- B'(7, -(-4)) → B'(7, 4)
- C'(7, -(-8)) → C'(7, 8)
- D'(3, -(-8)) → D'(3, 8)

So, after reflecting across the x-axis, the coordinates are:
- A'(3, 4)
- B'(7, 4)
- C'(7, 8)
- D'(3, 8)

3. **Reflect across the y-axis**:
When a point (x, y) is reflected across the y-axis, the new point becomes (-x, y):
- A''(-3, 4)
- B''(-7, 4)
- C''(-7, 8)
- D''(-3, 8)

Thus, the vertices of square A'B'C'D' after both reflections are:
- A''(-3, 4)
- B''(-7, 4)
- C''(-7, 8)
- D''(-3, 8)

The correct answer is that square A'B'C'D' has vertices:
- A'(-3, 4)
- B'(-7, 4)
- C'(-7, 8)
- D'(-3, 8)