Show that the point (0, -1, -1), (4 5, 1), (3, 9, 4) and (-4, 4, 4) are coplanar and find the equation of the common plane.

Explanation

To show that the points \( A(0, -1, -1) \), \( B(4, 5, 1) \), \( C(3, 9, 4) \), and \( D(-4, 4, 4) \) are coplanar, we will first find the equation of the plane that passes through points \( A \), \( B \), and \( C \). Then, we will check if point \( D \) satisfies this equation.

### Step 1: Write the equation of the plane through points \( A \), \( B \), and \( C \)

The general equation of a plane passing through three points \( A(x_1, y_1, z_1) \), \( B(x_2, y_2, z_2) \), and \( C(x_3, y_3, z_3) \) can be given by the determinant:

\[
\begin{vmatrix}
...