Statement-1 : The points A(-2,2), B(2,-2) and C(1,1) are the vertices of an obtuse angled isoscles triangle.
Statement-2: Every obtuse angle triangle is isosceles.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 not a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True

Explanation

To determine the validity of the statements regarding the points A(-2, 2), B(2, -2), and C(1, 1), we will analyze each statement step by step.

### Step 1: Calculate the lengths of the sides of the triangle formed by points A, B, and C.

We will use the distance formula to find the lengths of the sides AB, BC, and AC.

**Distance Formula:**
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

1. **Calculate AB:**
\[ AB = \sqrt{(2 - (-2))^2 + (-2 - 2)^2} = \sqrt{(2 + 2)^2 + (-2 - 2)^2} = \sqrt{4^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \]

2. **Calculate BC:**
\[ BC = \sqrt{(1 - 2)^2 + (1 - (-2))^2} = \sqrt{(-1)^2 + (1 + 2)^2} = \sqrt{1 + 3^2} = \sqrt{1 + 9} = \sqrt{10} \]

3. **Calculate AC:**
\[ AC = \sqrt{(1 - (-2))^2 + (1 - 2)^2} = \sqrt{(1 + 2)^2 + (1 - 2)^2} = \sqrt{3^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10} \]

### Step 2: Analyze the lengths of the sides.

From the calculations:
- \(AB = 4\sqrt{2}\)
- \(BC = \sqrt{10}\)
- \(AC = \sqrt{10}\)

We observe that \(BC = AC\), which indicates that the triangle is isosceles since two sides are equal.

### Step 3: Determine the type of triangle (acute, right, obtuse).

To determine if the triangle is obtuse, we can use the cosine rule. The cosine rule states:
\[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \]
Where \(C\) is the angle opposite side \(c\).

Let's find the angle at vertex C using the sides \(AB\), \(BC\), and \(AC\):
- Let \(c = AB = 4\sqrt{2}\)
- Let \(a = BC = \sqrt{10}\)
- Let \(b = AC = \sqrt{10}\)

Using the cosine rule:
\[ (4\sqrt{2})^2 = (\sqrt{10})^2 + (\sqrt{10})^2 - 2(\sqrt{10})(\sqrt{10})\cos(C) \]
Calculating each term:
\[ 32 = 10 + 10 - 20\cos(C) \]
\[ 32 = 20 - 20\cos(C) \]
Rearranging gives:
\[ 20\cos(C) = 20 - 32 \]
\[ 20\cos(C) = -12 \]
\[ \cos(C) = -\frac{3}{5} \]

### Step 4: Conclusion about the angle.

Since \(\cos(C) < 0\), angle C is obtuse (greater than 90 degrees).

### Final Statements:

- **Statement 1**: The points A(-2, 2), B(2, -2), and C(1, 1) are the vertices of an obtuse angled isosceles triangle. **(True)**
- **Statement 2**: Every obtuse angled triangle is isosceles. **(False)**

### Final Answer:
- Statement 1 is true.
- Statement 2 is false.