Skill: Reflect figures across the y-axis

To reflect a point across the $y$-axis, change the sign of its $x$-coordinate and keep its $y$-coordinate the same:

$$(x,y)\longrightarrow(-x,y)$$

This is like flipping the point over the $y$-axis. A point on the $y$-axis stays in the same place because its $x$-coordinate is $0$.

Example: Reflect triangle $ABC$ with vertices

$$A(-2,3),\qquad B(1,3),\qquad C(0,-2)$$

across the $y$-axis.

Apply the rule to each vertex:

1. For $A(-2,3)$, change $-2$ to $2$:

$$A'=(2,3)$$

2. For $B(1,3)$, change $1$ to $-1$:

$$B'=(-1,3)$$

3. For $C(0,-2)$, the $x$-coordinate is $0$, so the point stays fixed:

$$C'=(0,-2)$$

The reflected triangle has vertices

$$\boxed{A'(2,3),\ B'(-1,3),\ C'(0,-2)}$$

Notice that each point and its image are the same distance from the $y$-axis, and the image is the same shape and size as the original triangle.