https://file.aiquickdraw.com/mathbot/file/1727969801007hxjqcuao.jpg

The problem asks for the correct position of triangle \( Z \), which is obtained by reflecting triangle \( X \) across line \( P \) to form triangle \( Y \), and then reflecting triangle \( Y \) across line \( Q \) to get triangle \( Z \).

Here's how we can approach this:

1. **First Reflection (Triangle X to Y):** 
   - Triangle \( X \) is reflected in line \( P \). By looking at the provided diagrams, line \( P \) is a vertical line, which suggests a horizontal shift.
   - The reflection should mirror the triangle across line \( P \). This means triangle \( Y \) should be symmetrical to triangle \( X \), across this vertical line.

2. **Second Reflection (Triangle Y to Z):** 
   - Triangle \( Y \) is then reflected in line \( Q \), which appears to be a horizontal line based on the images provided.
   - This reflection will flip triangle \( Y \) vertically to produce triangle \( Z \).

Now, analyzing the options:
- We expect triangle \( Z \) to be positioned symmetrically to triangle \( Y \), based on the reflection across line \( Q \).

By visual inspection:
- The correct answer appears to be **option C** because it shows a reflection of triangle \( Y \) across the horizontal line \( Q \) after the vertical reflection from triangle \( X \) to \( Y \).

Would you like a more detailed breakdown of the reflection process?

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### Relative Questions:
1. How do reflections work across vertical and horizontal lines in coordinate geometry?
2. What properties of a triangle remain unchanged after reflection?
3. Can you generalize the rule for reflecting any shape across two perpendicular lines?
4. How do you identify the lines of reflection given a figure and its image?
5. How can multiple transformations, like reflections and rotations, affect a figure's orientation?

### Tip:
When reflecting across a line, think of the line as a "mirror" and imagine folding the grid along that line to visualize where the image will appear.

Triangle X is reflected in line P to give triangle Y. Triangle Y is then reflected in line Q to give triangle Z. Which diagram shows the correct position of triangle Z?

Learn how to find the correct position of triangle Z after reflecting triangle X in line P and then reflecting triangle Y in line Q. This problem covers key concepts in geometry, including reflections and symmetry in the coordinate plane. Suitable for students in Grades 7-9.

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