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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
A line and a point not on the line lie in exactly one plane?
True.
How many line can be drawn through two point in a plane?
One.
Can three points determined a plane?
Yes, three points determine a plane unless they are in a straight line. A plane is two dimensions a line is only one. You need a third point(not in the line) to define a plane.
Lines on a hyperbolic plane are considered to be?
Hyperbolic geometry is a beautiful example of non-Euclidean geometry. One feature of Euclidean geometry is the parallel postulate. This says that give a line and a point not on that line, there is exactly one line going through the point which is parallel to the line. (That is to say, that does NOT intersect the line) This does not hold in the hyperbolic plane where we can have many lines through a point parallel to a line. But then we must wonder, what do lines look like in the hyperbolic plane? Lines in the hyperbolic plane will either appear as lines perpendicular to the edge of the half-plane or as circles whose centers lie on the edge of the half-plane
A line and a point on a line always contain in one plane?
yah
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.
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.
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.
Point is to line as line is to?
Plane. A point has no dimension, a line has one dimension, and a plane has two dimensions.
When does a plane and line intersect at one point?
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.
What is true of a line and point not on the line?
The line and the point define a plane.
Do a line and a point not on that line lie in one and only one plane?
Yes because a line can lie in many planes so one we add one point not on that line, we define a unique plane.
Three what points determine a plane?
Any three points will determine a plane, provided they are not collinear. If you pick any two points, you can draw a line to connect them. An infinite number of planes can be drawn that include the line. But if you pick a third point that does not lie on the line. There will be exactly one plane that will contain the line and that point you added last. Only oneplane can contain the line, which was determined by the first two points, and the last point.
Is it true that only one plane can pass through one and a point that is not on the line?
If you mean "only one plane can pass through another plane and through a point that is not on the line formed by the intersection of the two planes," the answer is "no." If you rotate the plane about the point, it will still intersect the line unless it is parallel to the line. By rotating the plane, you have created other planes that pass through the unmoved plane and through the point that is not on the line formed by the intersection of the two planes.
Give a line and a point not on the line how many planes do they define?
They define one plane. A line is defined by two points, and it takes three points to define a plane, so two points on the line, and one more point not on the line equals one plane.
