Question 152386: A, B, C, and D are distinct coplanar points, no 3 of which are collinear. If E is a point not in the plane of A, B, C, and D, how many distinct planes are determined by the 5 points?
a. 4
b. 5
c. 6
d. 7
Which answer is correct and why?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Think about this!
Through any three non-collinear points, there is exactly one plane!
The planes that you identify here must include the point E, so you can list all of the possible combinations of the points, A, B, C, D, with the point E.
E,A,B
E,A,C
E,A,D
E,B,C
E,B,D
E,C,D
So it seems that there are 6 distinct planes determined by the five points if point E is to be included in each one.
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