Reflect figures across the y-axis

Reflection across the y-axis maps each point $(x,y)$ to $(-x,y)$ : the x-coordinate changes sign while the y-coordinate remains unchanged. The learner interprets this as producing a congruent mirror image with equal horizontal distances on opposite sides of the y-axis, recognizes that points on the y-axis remain fixed, and avoids the common error of changing the y-coordinate; the understanding applies to vertices and figures represented on the coordinate plane.

Detailed Explanation: 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.

Learn by doing: Reflect figures across the y-axis

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

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