https://file.aiquickdraw.com/mathbot/file/1730379395286xgixt7v8.jpg

To solve this, let's analyze the partially drawn square on the coordinate grid.

1. **Identify the known vertices of the square**:
   - From the image, we can observe that the red lines form an "L" shape with vertices at the coordinates (4, 7), (7, 7), and (7, 4).

2. **Determine the missing vertex**:
   - A square has four vertices with two sets of parallel lines of equal length.
   - The known vertices form two sides of the square:
     - One side from (4, 7) to (7, 7) (horizontal segment, 3 units in length).
     - Another side from (7, 7) to (7, 4) (vertical segment, also 3 units in length).
   - To complete the square, the missing vertex should be 3 units directly below the point (4, 7) or 3 units to the left of the point (7, 4).

3. **Calculate the missing vertex**:
   - Moving 3 units down from (4, 7) lands us at (4, 4).
   - So, the missing vertex is at **(4, 4)**.

4. **Check answer choices**:
   - None of the choices exactly list (4, 4) as an option. However, if the question is asking for a "closest" point or is intended as a trick to identify relative positioning, the answer might differ.

But based on direct analysis, **(4,4)** should logically be the missing vertex to complete the square. Let me know if there’s more you want on this.

Would you like more on this process?

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**Questions to Explore:**
1. What if the square was extended in the opposite direction?
2. How do we determine midpoint for irregular shapes?
3. How do transformations (rotation/reflection) affect coordinates in the grid?
4. Can we use distance formula here for verification?
5. How do different shapes relate in coordinate properties?

**Tip:** Visualizing coordinates and comparing distances can streamline spotting squares and symmetries.

Complete the square above. What are the coordinates of the missing vertex?

Learn how to find the missing vertex needed to complete a square on a coordinate grid. This problem explores coordinate geometry and the properties of squares, ideal for middle school students.

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