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Magazine Chapter 1: Q15WE. (page 25)
State whether it is possible for the figure described to exist. Write yes or no.
Three non-collinear points all lie in each of the two planes.
Short Answer
No, it is not possible that three non-collinear points all lie in each of two planes.
Step by step solution
Step 1. Write the postulate 7.
Postulate 7 states that through any three non-collinear points exactly one plane can pass.
Step 2. Draw the diagram of plane X passing through three non-collinear points A, B, and C.
The figure represents the plane passing through three non-collinear points , and is:
Step 3. State whether it is possible that three non-collinear points all lie in each of two planes by considering the postulate 7 and above diagram.
From the diagram and postulate 7, it can be noticed that if three points are non-collinear then exactly one plane can pass through these points. Therefore, it is not possible that any three non-collinear points can simultaneously lie on the two different planes.
Therefore, it is not possible that three non-collinear points all lie in each of the two planes.
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