Question

Rectangle has the points A:(-6,-2) B:(-2,-2)C:(-2,-5)D:(-6,-5) Reflect rectangle ABCD across the y-axis, and then the x-axis. What are the vertices of A'B'C'D'?

Answer 1

To reflect the rectangle ABCD across the y-axis and then the x-axis, we can follow these steps for each point:

1. **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 \((-x, y)\).

2. **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)