Final answer:
To create a plane in the middle of two existing planes, taking the average of the equations of those planes is the most accurate method, resulting in a new plane equidistant from both.
Step-by-step explanation:
To create a plane exactly in the middle of two existing planes/faces, the most mathematically accurate method is option 3) By taking the average of the equations of the two planes. If each plane can be defined by an equation in three-dimensional space, taking the average of these equations will yield a new equation that defines a plane equidistant from the two original planes. This method ensures that every point on the new plane is at the same distance from the respective closest points on the two original planes.
Option 1) By finding the intersection of the two planes will result in a line, not a plane. Option 2) By drawing a line segment between the two planes and finding its midpoint defines a point rather than a plane. Finally, option 4) By rotating one of the planes around an axis would not guarantee a plane in the middle unless the axis and angle were very specifically chosen, and even then, it would not be the straightforward method.