Question

consider points r, s, and t. which statement is true about the geometric figure that can contain these points? no line can be drawn through any pair of the points. one line can be drawn through all three points. one plane can be drawn so it contains all three points. two planes can be drawn so that each one contains all three points.

Explanation:

Step1: Recall geometric principles

In geometry, through any two - points, a line can be drawn. And through any three non - collinear points, exactly one plane can be drawn. We don't know if the three points R, S, and T are collinear or not, but we know that through any three points, at least one plane can be drawn.

Step2: Analyze each option

• Option 1: Lines can be drawn through pairs of points, so this is false.
• Option 2: We are not given that the points are collinear, so we can't say one line can be drawn through all three.
• Option 3: One plane can always be drawn to contain three points (either non - collinear or collinear as a collinear set of points is a subset of a plane), this is true.
• Option 4: There is exactly one plane that can contain three non - collinear points and if they are collinear, there are infinitely many planes containing them, not two in the general sense.

Answer:

One plane can be drawn so it contains all three points.