Skill: 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.

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