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Answer:
To determine the new coordinates of each vertex of a quadrilateral when it is reflected across the x-axis, you can follow these steps:
1. **Identify the Original Coordinates**: Note down the coordinates of the vertices of the quadrilateral. In this case, the vertices are:
- \( A (3, 4) \)
- \( B (5, 7) \)
- \( C (8, 2) \)
- \( D (6, -1) \)
2. **Understand the Reflection Rule**: When a point \((x, y)\) is reflected across the x-axis, its x-coordinate remains the same, but its y-coordinate changes sign. The new coordinates will be \((x, -y)\).
3. **Apply the Reflection Rule to Each Vertex**:
- For vertex \(A (3, 4)\), the new coordinates will be \((3, -4)\).
- For vertex \(B (5, 7)\), the new coordinates will be \((5, -7)\).
- For vertex \(C (8, 2)\), the new coordinates will be \((8, -2)\).
- For vertex \(D (6, -1)\), the new coordinates will be \((6, 1)\).
By following these steps, you can reflect any set of points across the x-axis without needing to perform detailed calculations each time. The key is to change the sign of the y-coordinate while keeping the x-coordinate unchanged.