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?

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.