Q12 - Geometry

Question

State a postulate, or part of a postulate, that justifies your answer to each exercise.

Does plane N contain any points not on $\overleftrightarrow{AB}$?

Step-by-Step Solution

Answer

Yes, plane N contains any points not on $\overleftrightarrow{\mathbf{A}\mathbf{B}}$.

Step 1. Write the postulate 6.

Postulate 6 is stated as “Through any two points there is exactly one line.”.

Step 2. Observe the diagram.

Now observing the given figure with two planes M and N, it can be seen that points that are labeled on plane M are B, A, C, and D, and points labeled on plane N are B and A.

Step 3. Relation between line AB and plane N.

A given plane consists of an infinite number of points and lines.

So, plane N contains a lot of points that are not on $\overleftrightarrow{AB}$.