Question

What is the greatest number of planes determined by four noncollinear points

Answer 1

4

Explanation:

Noncollinear points are points that do not lie on the same line.

Each three noncollinear points determine exactly one plane passing through these points.

Let A, B, c and D be four noncollinear points. Suppose that no three points are collinear. Then there can be built 4 planes:

• ABC
• ABD
• ACD
• BCD

If there are three points which are collinear, then there will be the only plane passing through the line connecting those three points and the fourth point.

Hence, the greatest number of planes determined by four noncollinear points is 4.