https://file.aiquickdraw.com/mathbot/file/1730237358758tdy2egm2.jpg

To determine the coordinates of \( Q'' \), let's go through the reflection steps provided in the problem.

### Step-by-Step Solution

1. **Identify Coordinates of \( Q \)**:
   - From the graph, the coordinates of \( Q \) are \( (1, 5) \).

2. **Reflect \( Q \) Across the x-axis to Form \( Q' \)**:
   - Reflecting across the x-axis changes the y-coordinate to its opposite (negative value), while the x-coordinate remains the same.
   - So, \( Q' \) will have coordinates \( (1, -5) \).

3. **Reflect \( Q' \) Across the y-axis to Form \( Q'' \)**:
   - Reflecting across the y-axis changes the x-coordinate to its opposite, while the y-coordinate stays the same.
   - Therefore, \( Q'' \) will have coordinates \( (-1, -5) \).

### Final Answer
The coordinates of \( Q'' \) are:
\[
(-1, -5)
\]

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

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### Related Questions
1. What are the coordinates of \( P'' \) after the same reflections?
2. What are the coordinates of \( R'' \) after the same reflections?
3. How would the coordinates change if we reflected \( \triangle PQR \) only across the y-axis?
4. How do reflections across both axes affect the orientation of a triangle?
5. How can we generalize the transformation rules for reflecting points across axes?

### Tip
For reflections: across the x-axis, the y-coordinate changes sign; across the y-axis, the x-coordinate changes sign.

Michael reflects ΔPQR across the x-axis to form ΔP'Q'R' and then across the y-axis to form ΔP''Q''R''. What are the coordinates of vertex Q''?

Learn how to reflect a triangle across the x-axis and y-axis on the coordinate plane. This example walks through finding the coordinates of Q'' after performing sequential reflections of ΔPQR. Suitable for students in Grades 6-8.

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