Which rule describes the transformation that is reflection across the $x$ axis?

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Solution

Reflection across the $x$ -axis:
The distance between the point and the reflected point from the $x$ -axis is same when the point is reflected about the $x$ -axis.
The $y$ -coordinate changes with the negative sign.
Hence, the rule for a reflection over the $x$ -axis is $(x, y) \to (x, - y)$ .

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