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The problem asks about reflecting triangle XYZ across the x-axis to find the coordinates of its new reflected points: \( X'', Y'', Z'' \).

When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. For a point \( (x, y) \), its reflection across the x-axis will be \( (x, -y) \).

Let’s apply this to each point:

1. **Point X''**: The original point is \( X''(-1, \_ ) \). Since the reflection only affects the y-coordinate, the y-value will change sign.
2. **Point Y''**: The original point is \( Y''(\_ , -1) \). The x-coordinate will remain the same, but the y-coordinate is given as \( -1 \), so the original point had a y-coordinate of 1.
3. **Point Z''**: The original point is \( Z''(-6, \_ ) \). The reflection will change the sign of the original y-coordinate.

Would you like to confirm the original coordinates of points \( X, Y, Z \), or should I proceed with solving based on this reflection rule? Let me know if you have any questions!

Here are 5 related questions you might consider:
1. How do we reflect a point across the y-axis?
2. What would happen if the triangle XYZ were reflected across the line \( y = x \)?
3. How would the coordinates change if the triangle were reflected across both the x-axis and y-axis?
4. How do you determine the distance between a point and its reflection?
5. What are other types of transformations besides reflections?

**Tip**: When reflecting across the x-axis, always remember that only the y-coordinate changes sign, not the x-coordinate!

Triangle XYZ is reflected across the x-axis to form figure X''Y''Z''. Determine the coordinates for points X'', Y'', and Z'' after reflection.

Understand how to reflect triangle XYZ across the x-axis, including the rules of reflection for each vertex. Learn to calculate the new coordinates of points X'', Y'', and Z'' after reflection. Ideal for students in Grades 6-8.

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