For what value of `k` are the points `(k ,2-2k)` `(k+1,2k)` and `(-4-k ,6-2k)` are collinear?

Explanation

To determine the value of \( k \) for which the points \( (k, 2-2k) \), \( (k+1, 2k) \), and \( (-4-k, 6-2k) \) are collinear, we can use the concept that three points are collinear if the area of the triangle they form is zero. The area can be calculated using the determinant of a matrix formed by the coordinates of the points.

### Step-by-Step Solution:

1. **Set up the determinant**:
The area of the triangle formed by the points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) can be expressed as:
\[
\text{Area} = \frac{1}{2} \begin{vmatrix}
...