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Is the intersection of a plane and a line always a point?
No. It can be the whole line.
Are a plane and a point not on the plane always coplanar?
No. In order to be coplanar, points have to be in the line.
Does a line always intersect a plane at one point?
yes
Does a plane containing two points of a line always never or sometimes contain the entire line?
It contains the whole line.
Only one plane can pass through one line and a point that is not on the line?
I'd feel a lot more comfortable if you said "... can contain one line and a point ...".When you say "pass through one line", I picture a sword passing through a tight pieceof string. If that's how your plane passes through the line, then the statement in your"question" is false. If your plane contains the line and the extra point, then the statementis true ... only one plane can do that.
Can a plane contain one point of a line?
Yes, it can. A plane can contain any number of points of a line.
Is the intersection of a plane and a line always a point?
No. It can be the whole line.
If a plane contains one point of a line then it must contain the entire line?
No, a plane can contain only one point of a line. Picture a piece of paper with a pencil stabbed through it. The paper is the plane, and the pencil is the line. The pencil/line only touches the paper/plane at one point. Hope this helped! If it did, please recommend me. -Brad
If a line intersects a plane that does not contain the line then the intersection is exactly one point?
Yes.
Are a plane and a point not on the plane always coplanar?
No. In order to be coplanar, points have to be in the line.
Does a line always intersect a plane at one point?
yes
Does a plane containing two points of a line always never or sometimes contain the entire line?
It contains the whole line.
What Point S is not on line k. How many different planes contain both point S and line k?
There is only one such plane.
Is the intersection of a line a point?
The intersection of two lines is always a point or the line itself. The intersection of a line with plane also the same as above.
How many lines can contain a line and a point not on the line?
In plane geometry a line is a two dimentional object between two points. If a line or a point is not on the line it, by definition, does not contain them. The answer therefor is infinite. Unless it is a closed line which has a slightly different definition but the answer is the same.
A plane and a line sometimes never or always intersect in a single point?
A given plane and a given line don't necessarily have to intersect at all.If the line is parallel to the plane, then they never do.The line can also be in the plane, and then every point on the line is alsoa point in the plane.The most likely case, though, is that the line is not parallel to the plane andnot in it. In that case, their intersection is a single point.So I guess the best answer from the allowed choices is 'sometimes'.
Only one plane can pass through one line and a point that is not on the line?
I'd feel a lot more comfortable if you said "... can contain one line and a point ...".When you say "pass through one line", I picture a sword passing through a tight pieceof string. If that's how your plane passes through the line, then the statement in your"question" is false. If your plane contains the line and the extra point, then the statementis true ... only one plane can do that.
