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Where does a plane and a line intersect?
In most cases, in a single point. It is also possible that there is no intersection, or that the intersection is the entire line.
how to negate the hyperbolic parallel postulate?
The hyperbolic parallel postulate states that given a line L and a point P, not on the line, there are at least two distinct lines through P that do not intersect L.The negation is that given a line L and a point P, not on the line, there is at most one line through P that does not intersect L.The negation includes the case where there is exactly one such line - which is the Euclidean space.
What are the 4 most basic geometric shapes?
A point, a line, a plane and a [3-d] space
Are two lines from the same plane parrellel?
They can be, but not necessarily. If two lines in the same plane never intersect, they are parallel. Though, two lines can exist in the same plane without being parallel. Ie, two lines that intersect at a 90 degree angle are perpendicular. Most lines in a plane aren't parallel.
What is correct about a line and a point A each can be col-linear B A point has no location and a line has many points located on it C each have no dimensions to measure D each on different planes?
More than one statement is correct about a line and a point:A line contains an infinite number of points.A line is the shortest distance, in Euclidean geometry, between two points.In a Euclidean geometry-defined universe, two lines can at most meet at one point (where they intersect; lines may also be askew in which case they do not meet at any point, meaning they do not live on the same plane).A point is a zero-dimensional entity (it possesses no length nor width nor height) which lives on 1D; a line is a one-dimensional entity (it possesses length but no width nor height) which lives on 2D.As we know, a line is the graph of the solution set of a linear equation. Each solution is a point on the line, and each point on the line is a solution to the equation.
A plane and a line intersect at most in one point?
Yes, except when the line is in the plane. In the latter case, they intersect at each point on the line (an infinite number).
Where does a plane and a line intersect?
In most cases, in a single point. It is also possible that there is no intersection, or that the intersection is the entire line.
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'.
What is the maximum number of times 2 planes can intersect?
In three-dimensional space, two planes can either:* not intersect at all, * intersect in a line, * or they can be the same plane; in this case, the intersection is an entire plane.
How can we rewrite Euclid's fifth postulate?
Euclid's fifth postulate: If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.It can be rewritten: If two lines are drawn which intersect a third at angles of 90 degrees, the two lines are parallel and will not intersect each other.It has also been rewritten as Playfair's axiom:In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
how to negate the hyperbolic parallel postulate?
The hyperbolic parallel postulate states that given a line L and a point P, not on the line, there are at least two distinct lines through P that do not intersect L.The negation is that given a line L and a point P, not on the line, there is at most one line through P that does not intersect L.The negation includes the case where there is exactly one such line - which is the Euclidean space.
What are the 4 most basic geometric shapes?
A point, a line, a plane and a [3-d] space
What is the maximum number of y intercepts that a line can have?
A line can have only one y-intercept. The y-intercept is the point at which the line intersects the y-axis on a graph, and it is determined by the equation of the line. Since a line can only intersect the y-axis at one point, it can have at most one y-intercept.
Are two lines from the same plane parrellel?
They can be, but not necessarily. If two lines in the same plane never intersect, they are parallel. Though, two lines can exist in the same plane without being parallel. Ie, two lines that intersect at a 90 degree angle are perpendicular. Most lines in a plane aren't parallel.
What is correct about a line and a point A each can be col-linear B A point has no location and a line has many points located on it C each have no dimensions to measure D each on different planes?
More than one statement is correct about a line and a point:A line contains an infinite number of points.A line is the shortest distance, in Euclidean geometry, between two points.In a Euclidean geometry-defined universe, two lines can at most meet at one point (where they intersect; lines may also be askew in which case they do not meet at any point, meaning they do not live on the same plane).A point is a zero-dimensional entity (it possesses no length nor width nor height) which lives on 1D; a line is a one-dimensional entity (it possesses length but no width nor height) which lives on 2D.As we know, a line is the graph of the solution set of a linear equation. Each solution is a point on the line, and each point on the line is a solution to the equation.
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
Who restated Euclid's 5th postulate?
Probably the best known equivalent of Euclid's parallel postulate, contingent on his other postulates, is Playfair's axiom, named after the Scottish mathematician John Playfair, which states:In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
