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:

According to the postulate in geometry, three non - collinear points (points that do not lie on the same straight line) determine a unique plane. In the case of points \(R\), \(S\), and \(T\) (assuming they are non - collinear as no indication of collinearity is given), one plane can be drawn to contain all three points.

• For the first option: A line can be drawn through any pair of points (by the postulate that two points determine a line).
• For the second option: Since the points are not shown to be collinear (lying on the same line), we cannot assume one line passes through all three.
• For the fourth option: Two planes cannot both contain the same three non - collinear points uniquely (by the plane - determination postulate for non - collinear points).

Answer:

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