Why must the three points used to name a plane not be collinear?

Conditions

• The three points are distinct.
• The points are being used to define or name a specific plane.

Reasoning, step by step

1. Consider three points that lie on one straight line.
2. Observe that multiple flat surfaces can rotate through that same line, so the plane is not uniquely determined.
3. Consider three points that are not in a straight line.
4. Conclude that only one plane goes through those three non-collinear points.

Example

The instructor states: 'if three points lie on one straight line, then more than one flat surface can pass through them, so the plane is not unique... Three points that are not on one line determine exactly one plane.'

Common misconceptions

• Thinking any three points determine exactly one plane.
• Assuming that collinear points define a unique plane just because they exist in space.

Watch the explanation

Explore next

• What are the two ways to name a plane shown in the lesson?
• How do you write a segment with endpoints X and Y?