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. select choice, the points do not have to be select choice 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

We know that there are many points in a plane. For example, consider a triangle drawn on a plane (like a sheet of paper). The three vertices of the triangle lie in the plane of the paper, but they are not collinear (since a triangle is defined by three non - collinear points). So, points that lie in a plane can be either collinear or non - collinear. That means the statement "If points M, N, and P lie in plane X, then they are collinear" is sometimes true. And the reason is that the points do not have to be collinear to lie in a plane.

Answer:

First "Select Choice": Sometimes
Second "Select Choice": collinear