Reflecting a point or a shape across the y-axis involves flipping it over the y-axis while keeping the y-coordinates the same and changing the sign of the x-coordinates.

Reflection Process

If you have a point $(x, y)$ and you want to reflect it across the y-axis, the reflected point will be $(-x, y)$.

Example

Let's say you have a point $(3, 5)$. To reflect this point across the y-axis:

• The x-coordinate changes sign: $3$ becomes $-3$.
• The y-coordinate remains the same: $5$ stays $5$.

So, the reflected point is $(-3, 5)$.

Steps for Reflecting a Shape

If you want to reflect an entire shape:

1. Identify the vertices of the shape.
2. Reflect each vertex across the y-axis by changing the sign of each x-coordinate while keeping the y-coordinates the same.
3. Connect the reflected vertices to form the new shape.

Example with a Triangle

Consider a triangle with vertices at $(2, 3)$, $(4, 6)$, and $(1, -2)$.

• Reflect $(2, 3)$ across the y-axis: it becomes $(-2, 3)$.
• Reflect $(4, 6)$ across the y-axis: it becomes $(-4, 6)$.
• Reflect $(1, -2)$ across the y-axis: it becomes $(-1, -2)$.

The reflected triangle will have vertices at $(-2, 3)$, $(-4, 6)$, and $(-1, -2)$.

Do you want details or have any questions? Here are some related questions to think about:

1. How would you reflect a point across the x-axis?
2. What happens to the coordinates when you reflect across the origin?
3. If you reflect a shape twice across the y-axis, where will it end up?
4. How does reflecting across the y-axis affect the distance between points?
5. Can you describe a situation where reflecting across the y-axis would be useful?

Tip: Visualizing reflections on graph paper can help you better understand how each point moves across the axis.