Question

suppose Point G represents a duck flying over a Lake, point H and J represent two ducks swimming on the lake. Which is a true statement?

Answer 1

Choice D. There is exactly one plane that contains the three ducks:
`\sf G`,
`\sf H`, and
`\sf J`.

Explanation:

The three points
`\sf G`,
`\sf H`, and
`\sf J` are distinct since each of the three points represents a different duck.

There's only one line through two distinct points in a 2D cartesian plane.

Likewise, given two distinct points (
`\sf G` and
`\sf J`) in a 3D space, there would be only one line two the two points.

Assume that plane
`\sf L` represents the plane that contains the surface of the lake.

A line is in a plane if and only if all points on that line are in the said plane.

Point
`\sf G` is on the line that contains
`\sf G\!` and
`\sf H`. However, since point
`\!\sf G` denotes the flying duck, this point would not be in
`\sf L` (the plane that contains the surface of the lake.)

Hence, the line that contains
`\sf G\!` and
`\sf H\!` would not be in plane
`\sf L\!`.

Given three distinct points in a 3D space, there would be exactly one plane that contains the three points.

Hence, three points in a 3D space would not be non-coplanar.

In this question, point
`\sf G`,
`\sf H`, and
`\sf J` are all distinct. Hence, there would be exactly one plane that contains these three points.