Determine whether the points (-9, 8, 1) (10.-15, 5), (6,6.-12), and (8. -4,-3) are coplanar.

These points are not coplanar

Step-by-step explanation:

The first step in determining whether these four points are coplanar is to find three vectors from these points.

Let's call A(-9,8,1), B(10,-15,5),C(6,6,-12) an D(8,-4,-3).

From these points, we can find the following vectors:

AB = B-A = (10,-15,5)-(-9,8,1) = (19,-23,4)

AC = C-A = (6,6,-12)-(-9,8,1) = (15,-2,-13)

AD = D-A = (8,-4,-3)-(-9,8,1) = (17,-12,-4)

If the mixed product of the vectors AB, AC and AD is equal to zero, then these points are coplanar.

Since the mixed product between these points is not zero, these points are not coplanar.

Answer and explanation:

Geometary software is merely a software implementation of solving the area of a triangle. Therefore geometry software employs all the methods used in coordinate algebra(manual) albeit behind the scenes, in the console of the software, and just displays the area in the screen after solving. While geometry software displays the area using automated methods in code, coordinate algebra solves area of the triangle manually using several steps. In both cases, we observe that algebra is required to solve area of the triangle as it is part of the algorithm used in the code for the geometry software. Also being able to use the geometry software requires that one understand coordinate algebra to be able to plot lines, points and planes at the correct locations on the screen and get desired result.