Given that these four points are coplanar so these four points lie on the same plane.

So first let us take three points and find the equation of the plane passing through these four points and then let us substitute the fourth point in it. If it is 0 then the point lies on the plane formed by these three points then they are coplanar.

The equation of the plane passing through these three points is given by the following equation.

Now let us take (0, – 1, – 1), (4, 5, 1), (3, 9, 4) and find plane equation.

Now apply the determinant

x(30 – 20) – (y + 1)(20 – 6) + (z + 1)(40 – 18) = 0

10x – (y + 1)(14) + (z + 1)(22) = 0

10x – 14y + 22z + 8 = 0 now divide by 2 on both sides

The equation is 5x – 7y + 11z + 4 = 0

Now let us substitute fourth point (– 4, 4, 4) we get

5(– 4) – 7(4) + 11(4) + 4 = 0

– 20 – 28 + 44 + 4 = 0

– 48 + 48 = 0

0 = 0

L.H.S = R.H.S

So as said above this fourth point satisfies so this point also lies on the same plane.

Hence they are coplanar.