https://file.aiquickdraw.com/mathbot/file/1730001531985gd9u8vvk.jpg

To determine the algebraic rule for the transformation shown, we observe the given points and their transformations:

1. Points \( T \), \( U \), and \( V \) reflect across the x-axis to become \( T' \), \( U' \), and \( V' \).
2. The original and transformed points have coordinates as follows:
   - \( T \) is at approximately \((-5, 1)\) and reflects to \( T' \) at \((-5, -1)\).
   - \( U \) is at approximately \((0, 5)\) and reflects to \( U' \) at \((0, -5)\).
   - \( V \) is at approximately \((5, 1)\) and reflects to \( V' \) at \((5, -1)\).

This shows that each point's y-coordinate has been negated, while the x-coordinate remains the same. This is a reflection over the x-axis.

### Algebraic Rule
The rule representing this transformation is:
\[
(x, y) \rightarrow (x, -y)
\]

Would you like more details or have any questions?

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Here are some related questions to expand on this topic:

1. What other transformations can be represented by algebraic rules?
2. How would a reflection over the y-axis be represented algebraically?
3. What is the rule for a rotation of 90 degrees around the origin?
4. How can we represent a translation in terms of algebraic rules?
5. What is the effect of combining multiple transformations on a figure?

**Tip:** When reflecting across the x-axis, only the y-coordinate changes sign, while the x-coordinate remains constant.

Which algebraic rule represents the transformation shown on the grid?

Learn how to determine the algebraic rule for a reflection transformation across the x-axis. This problem demonstrates key concepts in coordinate geometry and transformations, including the rule (x, y) → (x, -y). Suitable for students in Grades 8-10.

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