Q: Give a line and a point not on the line how many planes do they define?

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Yes because a line can lie in many planes so one we add one point not on that line, we define a unique plane.

No, planes intersect at a line.

From the concept of a point, one can define a line. Once the concept of a line is defined, one can define a plane. From the concept of a plane, any higher dimension geometrical object can be defined, e.g. a volume.

The line and the point define a plane.

Anything that contains the line must contain every point on the line, so "a point on the line" doesn't give us any more information. You're just asking how many planes can contain the line. Now imagine setting a wood panel down on a tight-rope. How many different ways can it set there before it falls off ? A lot, right ? An infinite number of planes can all contain your line. (And all of its points.)

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Yes because a line can lie in many planes so one we add one point not on that line, we define a unique plane.

No, planes intersect at a line.

Two planes intersect at a line

From the concept of a point, one can define a line. Once the concept of a line is defined, one can define a plane. From the concept of a plane, any higher dimension geometrical object can be defined, e.g. a volume.

The line and the point define a plane.

Anything that contains the line must contain every point on the line, so "a point on the line" doesn't give us any more information. You're just asking how many planes can contain the line. Now imagine setting a wood panel down on a tight-rope. How many different ways can it set there before it falls off ? A lot, right ? An infinite number of planes can all contain your line. (And all of its points.)

exactly 1

A single line is not sufficient to define a plane. You can find a plane such that the line is in it. But if you then rotate the plane using that line as the axis of rotation, you can get an infinite number of planes such that the line belongs to each and every one of the planes.

The intersection of three planes can be a plane (if they are coplanar), a line, or a point.

The intersection of two planes is a line. (or a massive explosion...lol)

You cannot define a line with a single point (a single point only defines itself). You need two points to define a line (and therefore to write the equation for it).

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