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To determine whether the quadrilateral formed by points \( A(-3,1) \), \( B(1,2) \), \( C(2,6) \), and \( D(-2,5) \) is a parallelogram, we need to calculate the slopes of opposite sides. If opposite sides have the same slope, then they are parallel, indicating that the shape is a parallelogram.

### Step 1: Calculate the Slopes of Each Side
The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

1. **Slope of \( AB \):**
   \[
   \text{slope of } AB = \frac{2 - 1}{1 - (-3)} = \frac{1}{4}
   \]

2. **Slope of \( CD \):**
   \[
   \text{slope of } CD = \frac{5 - 6}{-2 - 2} = \frac{-1}{-4} = \frac{1}{4}
   \]

   Since the slope of \( AB \) equals the slope of \( CD \), \( AB \parallel CD \).

3. **Slope of \( BC \):**
   \[
   \text{slope of } BC = \frac{6 - 2}{2 - 1} = \frac{4}{1} = 4
   \]

4. **Slope of \( DA \):**
   \[
   \text{slope of } DA = \frac{5 - 1}{-2 - (-3)} = \frac{4}{1} = 4
   \]

   Since the slope of \( BC \) equals the slope of \( DA \), \( BC \parallel DA \).

### Conclusion
Since both pairs of opposite sides are parallel, the quadrilateral is a **parallelogram**.

### Checking if the Parallelogram is a Rhombus
For a parallelogram to be a rhombus, all four sides must be of equal length. We’ll calculate the lengths of \( AB \), \( BC \), \( CD \), and \( DA \) using the distance formula:
\[
\text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

1. **Length of \( AB \):**
   \[
   AB = \sqrt{(1 - (-3))^2 + (2 - 1)^2} = \sqrt{4^2 + 1^2} = \sqrt{16 + 1} = \sqrt{17}
   \]

2. **Length of \( BC \):**
   \[
   BC = \sqrt{(2 - 1)^2 + (6 - 2)^2} = \sqrt{1^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17}
   \]

3. **Length of \( CD \):**
   \[
   CD = \sqrt{(-2 - 2)^2 + (5 - 6)^2} = \sqrt{(-4)^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17}
   \]

4. **Length of \( DA \):**
   \[
   DA = \sqrt{(-2 - (-3))^2 + (5 - 1)^2} = \sqrt{1^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17}
   \]

Since all four sides are equal, the parallelogram is also a **rhombus**.

### Answer
- **Do the points form a parallelogram?** Yes.
- **Is it also a rhombus?** Yes.

Would you like a detailed breakdown of any specific calculation? 

### Related Questions
1. How do you find the slope of a line given two points?
2. What are the properties of a parallelogram?
3. How do you distinguish between a parallelogram and a rhombus?
4. Can a square be classified as a rhombus and a rectangle? Why?
5. What is the relationship between slopes of parallel and perpendicular lines?

### Tip
When checking if a quadrilateral is a parallelogram, remember that opposite sides need to be parallel. For a rhombus, all sides must be equal in length.

Use slope to determine whether the quadrilateral with vertices A(-3,1), B(1,2), C(2,6), and D(-2,5) forms a parallelogram. If it is a parallelogram, determine if it is also a rhombus.

Calculate slopes to check if the quadrilateral with vertices A(-3,1), B(1,2), C(2,6), and D(-2,5) forms a parallelogram and verify if it is also a rhombus. This problem covers key concepts in analytic geometry, such as slope and distance formulas.

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