To reflect the rectangle ABCD across the y-axis and then the x-axis, we can follow these steps for each point:
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Reflect across the y-axis: To reflect a point \((x, y)\) across the y-axis, you change the sign of the x-coordinate, resulting in the point \((-x, y)\).
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Reflect across the x-axis: To reflect a point \((x, y)\) across the x-axis, you change the sign of the y-coordinate, resulting in the point \((x, -y)\).
Now, let's reflect each vertex of rectangle ABCD.
Step 1: Reflect across the y-axis
- \(A(-6, -2) \to A' (6, -2)\)
- \(B(-2, -2) \to B' (2, -2)\)
- \(C(-2, -5) \to C' (2, -5)\)
- \(D(-6, -5) \to D' (6, -5)\)
After reflecting across the y-axis, we have the new vertices:
- A': (6, -2)
- B': (2, -2)
- C': (2, -5)
- D': (6, -5)
Step 2: Reflect across the x-axis
Now we take the points \(A', B', C', D'\) and reflect them across the x-axis:
- \(A'(6, -2) \to A''(6, 2)\)
- \(B'(2, -2) \to B''(2, 2)\)
- \(C'(2, -5) \to C''(2, 5)\)
- \(D'(6, -5) \to D''(6, 5)\)
Summarizing, after reflecting across the x-axis, the vertices are:
- A'': (6, 2)
- B'': (2, 2)
- C'': (2, 5)
- D'': (6, 5)
Final Result
The final vertices of the rectangle A'B'C'D' after both reflections are:
- A'': (6, 2)
- B'': (2, 2)
- C'': (2, 5)
- D'': (6, 5)
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