Reflect points across the y-axis

Reflecting a point with integer coordinates across the $y$ -axis produces a point the same vertical distance from the axis on the opposite side: $(x,y)$ maps to $(-x,y)$ . The $x$ -coordinate changes sign while the $y$ -coordinate remains unchanged, and points on the $y$ -axis stay fixed; this establishes coordinate symmetry without extending to more advanced transformation rules.

Detailed Explanation: Reflect points across the y-axis

To reflect a point across the $y$ -axis:

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

The rule is

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

Example

Reflect the point $(A(3,-2))$ across the $y$ -axis.

The $x$ -coordinate is $3$ . Change its sign to get $(-3)$ .
Keep the $y$ -coordinate, $(-2)$ , unchanged.
Write the new point:

A'( -3,-2)

So, the reflection of $(A(3,-2))$ across the $y$ -axis is

\boxed{A'(-3,-2)}

The original point and its reflection are the same distance from the $y$ -axis, but they are on opposite sides. A point already on the $y$ -axis stays in the same place.

Learn by doing: Reflect points across the y-axis

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

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