https://file.aiquickdraw.com/mathbot/file/1729522940632co0tf7ly.jpg

Let's work through the problem shown in the image:

### (a) Reflecting points across the y-axis
For reflection across the y-axis, the rule is:
- \( (x, y) \rightarrow (-x, y) \)
This means the x-coordinate changes its sign, but the y-coordinate remains the same.

Using this rule, we can find the coordinates for \( D' \), \( E' \), and \( F' \):

1. \( D(-7, -3) \rightarrow D'(7, -3) \)
2. \( E(-8, 6) \rightarrow E'(8, 6) \)
3. \( F(-2, 5) \rightarrow F'(2, 5) \)

### (b) General rule for reflection
As we determined from part (a), the rule for reflecting a point across the y-axis is:
- \( (x, y) \rightarrow (-x, y) \)

So, the correct answer is:
- \( (x, y) \rightarrow (-x, y) \)

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Do you want any more detailed explanations or have any questions?

Here are some related questions for you to consider:
1. What happens when you reflect a point across the x-axis?
2. How would you reflect a point across the origin?
3. What if we reflected the triangle over the line \( y = x \)? How would the points change?
4. What happens to the orientation of the shape after reflection across an axis?
5. How would reflecting over both axes change the points' coordinates?

**Tip**: When reflecting a point, always think about which axis (or line) is used and how it affects the x- or y-coordinates.

Triangle DEF is reflected across the y-axis. What are the new coordinates of D', E', and F'? What is the general rule for reflecting a point across the y-axis?

Learn how to reflect Triangle DEF across the y-axis and find the new coordinates for D', E', and F'. This problem covers key geometric concepts, including the reflection formula for coordinates. Suitable for students in Grades 6-8.

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