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To solve this reflection problem, we need to identify the line of reflection and the transformation rule that maps one triangle onto the other.

### Step-by-Step Solution:

1. **Identify the line of reflection**:
   - The line of reflection appears to be the line \( y = x \), as the triangle in blue and the triangle in black are symmetric across this line.
   
2. **Determine the reflection rule**:
   - For a reflection across the line \( y = x \), the coordinates \((x, y)\) of any point are transformed to \((y, x)\).
   - Therefore, the reflection rule is \( r_t(x, y) = (y, x) \).

3. **Equation of the reflection line**:
   - The equation of the line \( t \) is \( y = x \).

### Answer:
The reflection rule is:
\[
r_t(x, y) = (y, x)
\]
where the equation of line \( t \) is \( y = x \).

Would you like more details on this problem, or do you have any questions?

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### Related Questions

1. How do you find the line of reflection when given two shapes?
2. What are other common reflection rules for different reflection lines?
3. How does reflecting over \( y = -x \) differ from reflecting over \( y = x \)?
4. Can the distance between corresponding points help verify a reflection?
5. How would this transformation rule change if the line of reflection were horizontal or vertical?

### Tip:
When reflecting a point across the line \( y = x \), remember that you simply swap the coordinates of the point.

What is a reflection rule that maps each triangle and its image?

Learn how to find the reflection rule that maps a triangle onto its image and identify the line of reflection. This problem focuses on reflection transformations across the line y = x, suitable for Grades 8-10.

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