To find the coordinates of the vertices after reflecting each point across the y-axis, we need to apply the reflection rule for the y-axis.

When a point $(x, y)$ is reflected over the y-axis, its x-coordinate changes sign, while the y-coordinate remains the same. Thus, the reflected point will be $(-x, y)$.

Given points:

• $A(2, 5)$
• $B(1, 2)$
• $C(3, 1)$

Let's reflect each point:

1. Reflect $A(2, 5)$ across the y-axis: $A' = (-2, 5)$

2. Reflect $B(1, 2)$ across the y-axis: $B' = (-1, 2)$

3. Reflect $C(3, 1)$ across the y-axis: $C' = (-3, 1)$

Coordinates of the image after reflection:

• $A' = (-2, 5)$
• $B' = (-1, 2)$
• $C' = (-3, 1)$

Would you like further details on this process, or have any questions?

Here are five related questions that expand on this information:

1. What would be the coordinates if we reflected the points across the x-axis instead?
2. How would the coordinates change if we reflected them across the line $y = x$?
3. What is the general rule for reflecting a point over any arbitrary vertical line, such as $x = 4$?
4. How would you find the coordinates if you performed a rotation of 180 degrees instead of a reflection?
5. What transformations leave the coordinates of a point unchanged?

Tip: Reflections over the y-axis only affect the x-coordinates, while the y-coordinates remain unchanged.