Q17. - Geometry

Question

Classify each statement as true or false.

It is possible to locate three points in such a position that an unlimited number of planes contain all three points.

Step-by-Step Solution

Answer

The given statement that It is possible to locate three points in such a position that an unlimited number of planes contain all three points is True.

Step 1. Write the Postulate 7.

The Postulate 7 states that there is at least one plane passing through any three points and through any three non collinear points, exactly one plane passes.

Step 2. Draw three collinear points and planes passing through these points.

Step 3. State whether the given statement is true or false by considering the postulate 7 and the diagram.

From the diagram and postulate 7 it can be concluded that:

If there are three non collinear points then exactly one plane can pass through these points but if there are three collinear points then infinite planes can pass through these points.

Therefore, if the three points are collinear then it is possible to draw an unlimited number of planes passing through these points.

Hence the given statement that It is possible to locate three points in such a position that an unlimited number of planes contain all three points is true.