Reflect figures across the y-axis

Reflecting a figure across the y-axis maps each point $(x, y)$ to $(-x, y)$ : the x-coordinate changes sign while the y-coordinate remains unchanged. The image is congruent to the original and lies the same perpendicular distance from the y-axis, with points on the y-axis remaining fixed; this understanding supports coordinate proofs and reasoning about rigid transformations.

Detailed Explanation: 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:

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

A'=(2,3)

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

B'=(-1,3)

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.

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

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Reflect figures across the y-axis

Detailed Explanation: Reflect figures across the y-axis

Learn by doing: Reflect figures across the y-axis

Practice with unlimited practice problems

Practice:

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