Are a line and a point not on the line sometimes or always coplanar?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A line and a point not on the line are always coplanar. This follows from the fact that to define a plane we need three distinct points.

Or putting it in another way, it is always possible to draw a plane through any three points. Though if we have four points one of them may not lie on the plane that is drawn using the other three points.

To define a line we only need two distinct points. In your problem, we have two points that lie on the given line and another point not lying on the line. These three points always define a unique plane.

Therefore, a line and a point not lying on the line are always coplanar.

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