Reflect points across the x-axis

Reflection across the x-axis maps a point $(x,y)$ to $(x,-y)$ : the x-coordinate remains unchanged, while the y-coordinate changes sign, reversing its position above or below the x-axis. Points on the x-axis are unchanged, and the original and reflected points are the same distance from that axis; this understanding connects coordinate transformations to symmetry and later work with geometric rules and equations.

Detailed Explanation: Reflect points across the x-axis

To reflect a point across the x-axis:

Keep the x-coordinate the same.
Change the sign of the y-coordinate.

The rule is

(x,y)\rightarrow(x,-y)

Example

Reflect the point $A(-3,4)$ across the x-axis.

Keep the x-coordinate, $-3$ .
Change the sign of the y-coordinate, $4$ to $-4$ .
Write the reflected point:

A'(-3,-4)

So, the reflection of $A(-3,4)$ across the x-axis is $\boxed{(-3,-4)}$ .

The original point is 4 units above the x-axis, and the reflected point is 4 units below it.

Learn by doing: Reflect points across the x-axis

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Cartesian Grid - Reflection of Point (Grid to Coordinates) across Axis

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