There can be only one plane through any 3 noncollinear points. (If the three points are collinear then there are an infinite number of planes through the three points -- imagine a line along the spine of a book and the pages as planes.)

With that, we can show that through a line and a point not on the line there is exactly 1 plane. In all four cases shown, there is exactly 1 plane. (Note that the plane need not be drawn in the diagram.)

If one of the questions had been the number of planes through the line AB and point C, the answer would be infinite.

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The answer is the same for all four parts -- there is exactly one plane through the given line and point.

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A line is uniquely defined by 2 points. There cannot be more than one one equation of a line that passes through two given points, though the same equation could be written in an infinite number of different forms.

Similarly, a plane is uniquely defined by 3 points. Only one plane can pass through any three points that are given.

**There is only one plane each that contains the line and point given.**