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.
There are two possible answers; if the line is crossing the plane at an angle, then the line and the plane only intersect at one point. However, if the line is part of the plane, then the entire line intersects with the plane, and there are an infinite number of intersecting points.
False. They can only be straight line segments: there cannot be any curved line segments.
True for the Euclidean plane. There are consistent geometries (for example, projective geometry, or on the surface of a sphere where there may be none or more than one such lines.
Yes because a line can lie in many planes so one we add one point not on that line, we define a unique plane.
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.
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
There is only one such 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.
False - there were 3 sections of the plane that survived.
If the line is not IN the plane ... it just zaps through the plane from some direction ... then it touches the plane in only one point. The intersection is a point.if it is lined up with the plane, then the intersection is a line.
There are two possible answers; if the line is crossing the plane at an angle, then the line and the plane only intersect at one point. However, if the line is part of the plane, then the entire line intersects with the plane, and there are an infinite number of intersecting points.
False. They can only be straight line segments: there cannot be any curved line segments.
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.
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.
True for the Euclidean plane. There are consistent geometries (for example, projective geometry, or on the surface of a sphere where there may be none or more than one such lines.
No. A line can lie in many planes. A plane can be defined by three non-linear points. Since a line is defined by only two points, we need another point. (Note that point C alone, or line AB alone belong to an infinite number of planes.)