The points A(3,1) , B (12,-2) and C(0,2) cannot be vertices of a triangle.

Explanation

To determine whether the points A(3,1), B(12,-2), and C(0,2) can be the vertices of a triangle, we need to find the area of the triangle formed by these three points. If the area is zero, it means the points are collinear and cannot form a triangle.

### Step-by-Step Solution:

1. **Identify the Coordinates:**
- Let the coordinates of the points be:
- A(x₁, y₁) = A(3, 1)
- B(x₂, y₂) = B(12, -2)
- C(x₃, y₃) = C(0, 2)

2. **Use the Area Formula:**
- The formula for the area of a triangle given vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:
\[ \text{Area} = \frac{1}{2} \left| x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) \right| \]

3. **Substitute the Values:**
- Substitute the coordinates into the formula:
\[ \text{Area} = \frac{1}{2} \left| 3((-2) - 2) + 12(2 - 1) + 0(1 - (-2)) \right| \]

4. **Calculate Each Term:**
- Calculate the first term:
\[ 3((-2) - 2) = 3(-4) = -12 \]
- Calculate the second term:
\[ 12(2 - 1) = 12(1) = 12 \]
- The third term is:
\[ 0(1 - (-2)) = 0 \]

5. **Combine the Terms:**
- Now combine the calculated terms:
\[ \text{Area} = \frac{1}{2} \left| -12 + 12 + 0 \right| = \frac{1}{2} \left| 0 \right| = 0 \]

6. **Conclusion:**
- Since the area of the triangle is 0, the points A, B, and C are collinear. Therefore, they cannot be the vertices of a triangle.

### Final Answer:
The statement is **True**: The points A(3,1), B(12,-2), and C(0,2) cannot be vertices of a triangle.