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