When a point \((x, y)\) is reflected across the \(y\)-axis, its \(x\)-coordinate changes sign while the \(y\)-coordinate remains the same.
Let's apply this to the two given points:
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For the point \((6, -3)\):
- The reflection across the \(y\)-axis is \((-6, -3)\).
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For the point \((3, 1)\):
- The reflection across the \(y\)-axis is \((-3, 1)\).
Therefore, the new points after the reflection are \((-6, -3)\) and \((-3, 1)\).
The correct response is: \((-6, -3)\) and \((-3, 1)\).