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: Analyze the first option

A line can be drawn through any two points. So, the statement “No line can be drawn through any pair of the points” is false.

Step2: Analyze the second option

Since the three points \(R\), \(S\), and \(T\) are not collinear (from the given figure), a single line cannot pass through all three points. So, the statement “One line can be drawn through all three points” is false.

Step3: Analyze the third option

According to the postulate, three non - collinear points lie on exactly one plane. Since \(R\), \(S\), and \(T\) are non - collinear points, one plane can be drawn so it contains all three points. This statement is true.

Step4: Analyze the fourth option

Three non - collinear points determine a unique plane. So, the statement “Two planes can be drawn so that each one contains all three points” is false.

Answer:

One plane can be drawn so it contains all three points