Question

construct arguments determine whether the statement is always, sometimes, or never true. justify your argument. if points m, n, and p lie in plane x, then they are collinear. always the points do not have to be collinear to lie in a plane.

Explanation:

Step1: Recall plane and collinear definitions

A plane is a flat, two - dimensional surface that extends infinitely far. Collinear points are points that lie on the same straight line.

Step2: Analyze the relationship between points in a plane and collinearity

We can have three points in a plane that form a triangle (for example, the vertices of a triangle lie in the same plane but are not collinear). So, three points in a plane are not always collinear; they can be collinear (sometimes) or non - collinear. So the statement "If points M, N, and P lie in plane X, then they are collinear" is sometimes true because the points do not have to be collinear to lie in a plane.

Answer:

The first dropdown should be "Sometimes" and the second dropdown should be "collinear" (the reasoning is that three points in a plane can be collinear (e.g., three points on a straight line in the plane) or non - collinear (e.g., vertices of a triangle in the plane), so the statement is sometimes true as the points don't have to be collinear to be in the plane).