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 postulates

Through any two - points, a line can be drawn. So the statement "No line can be drawn through any pair of the points" is false.

Step2: Analyze collinearity

Three non - collinear points do not lie on the same line. Since we have no information that points R, S, and T are collinear, the statement "One line can be drawn through all three points" is not always true.

Step3: Apply plane - point postulate

The postulate states that through any three non - collinear points, there is exactly one plane, and if the points are collinear, there are infinitely many planes passing through them. In either case, one plane can be drawn to contain all three points.

Step4: Understand uniqueness of a plane for three points

It is not possible to have two distinct planes that each contain exactly the same three non - collinear points. If the points are collinear, there are infinitely many planes, but not exactly two.

Answer:

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