Skill: Reflect figures across the y-axis

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

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

Change the sign of the $x$-coordinate, but keep the $y$-coordinate the same. This places the point the same horizontal distance on the opposite side of the $y$-axis.

Example

Reflect triangle $(ABC)$ with vertices

$$A(0,2),\qquad B(3,1),\qquad C(2,4)$$

across the $y$-axis.

Apply the rule to each vertex:

• $(A(0,2)\rightarrow A'(0,2))$
  The point stays fixed because it is already on the $y$-axis.

• $(B(3,1)\rightarrow B'(-3,1))$
  Change $3$ to $(-3)$, and keep $1$.

• $(C(2,4)\rightarrow C'(-2,4))$
  Change $2$ to $(-2)$, and keep $4$.

So the reflected triangle has vertices

$$A'(0,2),\qquad B'(-3,1),\qquad C'(-2,4).$$

When you graph the new points and connect them, the result is a congruent mirror image of the original triangle. Remember: for a reflection across the $y$-axis, only the $x$-coordinate changes sign.