https://file.aiquickdraw.com/mathbot/file/17301563608484u4fhnar.jpg

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?

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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.

The vertices of a triangle are A(2, 5), B(1, 2), and C(3, 1). Find the coordinates of the image after a reflection in the y-axis.

Find the coordinates of the triangle vertices A(2, 5), B(1, 2), and C(3, 1) after reflecting them across the y-axis. This problem demonstrates key concepts in coordinate geometry, particularly reflections.

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