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What is an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line?
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line (-7,3); x=4
To find a segment parallel to another segment and through a given point fold a piece of paper so that the fold goes through the point fold a piece of paper so that thefold goes through the point?
true
How do you write an equation for a line that passes through point and is parallel to the given line?
Both straight line equations will have the same slope or gradient but the y intercepts wll be different
Why don't parallel lines exist in elliptical geometry?
Elliptical geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry was replaced by the statement that through any point in the plane, there exist no lines parallel to a given line. A consistent geometry - of a space with positive curvature - was developed on that basis.It is, therefore, by definition that parallel lines do not exist in elliptical geometry.
What is the equation of the line that passes through (1 2) and is parallel to the line whose equation is 4x plus y - 1 0?
Without an equality sign the given terms can't be considered to be an equation but in general when lines are parallel they have the same slope but different y intercepts.
What does the following Define through a given point not a given line there is exactly one line parallel to the given line?
The statement means that through any point not located on a given line, there is exactly one line that can be drawn that is parallel to the original line. This is a fundamental concept in Euclidean geometry, often referred to as the Parallel Postulate. It asserts that the parallel line will never intersect the given line, maintaining a constant distance apart from it. This principle underlies many geometric constructions and proofs.
Through a given point not on a given line there is exactly one line parallel to the given line?
The Playfair Axiom (or "Parallel Postulate")
Through a given point not a given line there is exactly one line parallel to the give line?
This statement is a fundamental concept in Euclidean geometry, often referred to as the Parallel Postulate. It asserts that for any given line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This principle establishes the uniqueness of parallel lines in a flat, two-dimensional space, meaning that no other line can be parallel to the given line through that specific point.
In Euclidean geometry if there is a line and a point not on the line then there is exactly one line through the point and the parallel to the given line. True or false?
True. In Euclidean geometry, if there is a line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This is known as the Parallel Postulate, which states that for a given line and a point not on it, there is one and only one line parallel to the given line that passes through the point.
What is another name for the Playfair Axiom?
Another name for the Playfair Axiom is the Euclid's Parallel Postulate. It states that given a line and a point not on that line, there is exactly one line parallel to the given line passing through the given point.
What is elliptical geometry and examples?
Elliptical geometry is like Euclidean geometry except that the "fifth postulate" is denied. Elliptical geometry postulates that no two lines are parallel.One example: define a point as any line through the origin. Define a line as any plane through the origin. In this system, the first four postulates of Euclidean geometry hold; through two points, there is exactly one line that contains them (i.e.: given two lines through the origin, there is one plane that contains them) and so on. However, it is nottrue that given a line and a point not on the line that there is a parallel line through the point (that is, given a plane through the origin, and a line through the origin, not on the plane, there is no other plane through the origin that is parallel to the given plane).
How do you negate the euclidean parallel postulate?
Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.
What is an example of an postulate?
An example of a postulate is the "Parallel Postulate" in Euclidean geometry, which states that through any point not on a given line, there is exactly one line that can be drawn parallel to the given line. This postulate serves as a foundational assumption for the development of Euclidean geometry and is critical in understanding the properties of parallel lines.
Which conjecture justifies the construction of a line parallel to a given line through a given point?
Euclid's parallel postulate.
Is hyperbolic parallel postulate a postulate of Euclid?
No, the hyperbolic parallel postulate is not one of Euclid's original five postulates. Euclid's fifth postulate, known as the parallel postulate, states that given a line and a point not on that line, there is exactly one line parallel to the original line that passes through the point. Hyperbolic geometry arises from modifying this postulate, allowing for multiple parallel lines through the given point, leading to a different set of geometric principles.
How many lines are parallel to a given line through a given point?
zero
Through a point not on the line exactly one line can be drawn parallel to the?
... given line. This is one version of Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.
