https://file.aiquickdraw.com/mathbot/file/1726682887340t6aa3tk2.jpg

Let's analyze the problem from the image.

The diagram shows a circle \( W \) with its diameter \( XY \) plotted on the coordinate plane. We need to find the correct statement about the center of the circle and the length of the diameter.

### Steps:
1. **Identify the coordinates of points \( X \) and \( Y \):**
   - From the graph, \( X \) is at (3, -2) and \( Y \) is at (1, -2).

2. **Find the center of the circle:**
   - The center of the circle lies at the midpoint of \( XY \).
   - The midpoint formula is:
     \[
     \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
     \]
   - Substituting \( X(3, -2) \) and \( Y(1, -2) \):
     \[
     \text{Midpoint} = \left( \frac{3 + 1}{2}, \frac{-2 + (-2)}{2} \right) = (2, -2)
     \]
   - Therefore, the center of the circle is at \( (2, -2) \).

3. **Calculate the length of the diameter:**
   - The distance formula between two points is:
     \[
     d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
     \]
   - Substituting \( X(3, -2) \) and \( Y(1, -2) \):
     \[
     d = \sqrt{(3 - 1)^2 + (-2 - (-2))^2} = \sqrt{(2)^2 + (0)^2} = \sqrt{4} = 2
     \]
   - The diameter of the circle is 2 units.

### Conclusion:
The center of the circle is at \( (2, -2) \) and the diameter is 2 units. Therefore, none of the answer choices given are exactly correct, as all diameter lengths differ from 2 units.

Would you like further clarification or details on this problem?

### Related questions:
1. How do you find the radius from the diameter of a circle?
2. How would the equation of this circle look if expressed in standard form?
3. What is the significance of the midpoint in circle geometry?
4. How can you calculate the circumference of this circle based on the diameter?
5. What is the formula for finding the area of a circle, and how does it apply here?

### Tip:
To verify the center of a circle on a coordinate plane, always use the midpoint of the diameter!

Which statement about the center of circle W and the length of the diameter is true?

Learn how to find the center and diameter of a circle on a coordinate plane. This problem uses the midpoint and distance formulas to calculate the coordinates of the center and the length of the diameter. Suitable for students in Grades 8-10.

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